Rug Arch

Package ‘rugarch’January 2, 2012 Type Package Title Univariate GARCH models Version 1.0-7 Date 2011-12-16 Author Alexios Ghalanos <[email protected]> Maintainer Alexios Ghalanos <[email protected]> Depends R (>= 2.10.0), Rcpp (>= 0.8.5), RcppArmadillo (>= 0.2.5),methods, numDeriv, chron, Rsolnp LinkingTo Rcpp, RcppArmadillo Description ARFIMA, in-mean, external regressors and various GARCH flavours, with methods for fit, forecast, simulation, inference and plotting. SystemRequirements GNU make Suggests xts, timeSeries, multicore, snowfall Collate rugarch-imports.R rugarch-cwrappers.R rugarch-solvers.R rugarch-distributions.R rugarch-kappa.R rugarch-helperfn.R rugarch-numderiv.R rugarch-series.R rugarch-startpars.R rugarch-tests.R rugarch-armafor.R rugarch-graphs.R rugarch-classes.R rugarch-sgarch.R rugarch-fgarch.R rugarch-egarch.R rugarch-gjrgarch.R rugarch-aparch.R rugarch-igarch.R rugarch-multi.R rugarch-plots.R rugarch-rolling.R rugarch-uncertainty.R rugarch-bootstrap.R rugarch-methods.R rugarch-benchmarks.R arfima-classes.R arfima-multi.R arfima-main.R arfima-methods.R zzz.R LazyLoad yes License GPL-3 Repository CRAN 1 2 Repository/R-Forge/Project rgarch Repository/R-Forge/Revision 369 Date/Publication 2011-12-24 12:10:35 R topics documented: R topics documented: rugarch-package . . . . . . . ARFIMA-class . . . . . . . ARFIMAdistribution-class . arfimadistribution-methods . ARFIMAfilter-class . . . . . arfimafilter-methods . . . . . ARFIMAfit-class . . . . . . arfimafit-methods . . . . . . ARFIMAforecast-class . . . arfimaforecast-methods . . . ARFIMAmultifilter-class . . ARFIMAmultifit-class . . . ARFIMAmultiforecast-class ARFIMAmultispec-class . . ARFIMApath-class . . . . . arfimapath-methods . . . . . ARFIMAroll-class . . . . . arfimaroll-methods . . . . . ARFIMAsim-class . . . . . arfimasim-methods . . . . . ARFIMAspec-class . . . . . arfimaspec-methods . . . . . BerkowitzLR . . . . . . . . DACTest . . . . . . . . . . . dji30ret . . . . . . . . . . . dmbp . . . . . . . . . . . . ForwardDates-methods . . . GARCHboot-class . . . . . GARCHdistribution-class . . GARCHfilter-class . . . . . GARCHfit-class . . . . . . . GARCHforecast-class . . . . GARCHpath-class . . . . . GARCHroll-class . . . . . . GARCHsim-class . . . . . . GARCHspec-class . . . . . GARCHtests-class . . . . . ghyptransform . . . . . . . . multifilter-methods . . . . . multifit-methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 7 8 10 11 13 14 17 18 21 22 23 23 24 25 26 27 29 29 30 31 33 35 36 37 37 38 39 40 40 41 42 42 43 44 44 45 46 47 rugarch-package multiforecast-methods . . . multispec-methods . . . . . rGARCH-class . . . . . . . rgarchdist . . . . . . . . . . sp500ret . . . . . . . . . . . ugarchbench . . . . . . . . . uGARCHboot-class . . . . . ugarchboot-methods . . . . uGARCHdistribution-class . ugarchdistribution-methods . uGARCHfilter-class . . . . . ugarchfilter-methods . . . . uGARCHfit-class . . . . . . ugarchfit-methods . . . . . . uGARCHforecast-class . . . ugarchforecast-methods . . . uGARCHmultifilter-class . . uGARCHmultifit-class . . . uGARCHmultiforecast-class uGARCHmultispec-class . . uGARCHpath-class . . . . . ugarchpath-methods . . . . . uGARCHroll-class . . . . . ugarchroll-methods . . . . . uGARCHsim-class . . . . . ugarchsim-methods . . . . . uGARCHspec-class . . . . . ugarchspec-methods . . . . WeekDayDummy-methods . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 48 49 50 50 52 53 54 55 57 58 60 61 63 66 68 69 71 71 72 73 74 75 76 78 80 81 83 84 87 88 rugarch-package The rugarch package Description The rugarch package aims to provide a flexible and rich univariate GARCH modelling and testing environment. Modelling is a simple process of defining a specification and fitting the data. Inference can be made from summary, various tests and plot methods, while the forecasting, filtering and simulation methods complete the modelling environment. Finally, specialized methods are implemented for simulating parameter distributions and evaluating parameter consistency, and a bootstrap forecast method which takes into account both parameter and predictive distribution uncertainty. The testing environment is based on a rolling backtest function which considers the more general context in which GARCH models are based, namely the conditional time varying estimation of density parameters and the implication for their use in analytical risk management measures. The mean equation allows for AR(FI)MA, arch-in-mean and external regressors, while the variance equation implements a wide variety of univariate GARCH models as well as the possibility quantile. The type of data handled by the package is quite varied. “xts”. the interested user can search the rugarch. bootstrap forecast ugarchboot and rolling estimation and forecast ugarchroll.0). sampling and fitting. parameter distribution by simulation ugarchdistribution. forecasting ugarchforecast. numDeriv. ghyptransform function provides the necessary parameter transformation and scaling methods for moving from the location scale invariant ‘rho-zeta’ parametrization with mean and standard deviation. “data. and neither is a forecast based on the bootstrap. no representation is made about the adequacy of ARFIMA models.frame” with characterdates in names or rownames. there is no guarantee of convergence in the fitting procedure. a set of rich distributions from the “fBasics” package and Johnson’s reparametrized SU from the “gamlss” package are used for modelling innovations.10. particularly the statistical properties of parameters when using distributions which go beyond the Gaussian. with the exception that no plots are yet implemented.8. There are also some functions which enable multiple fitting of assets in an easy to use wrapper with the option of multicore functionality.2. chron.4 rugarch-package of including external regressors. This subset includes similar functionality as with the GARCH methods. “zooreg”. This package is part of what used to be the rgarch package. While there are limited examples in the documentation on the ARFIMA methods. accepting “timeSeries”. As a result. RcppArmadillo (>= 0. For the “numeric” vector and “data. Rcpp (>= 0. A separate subset of methods and classes has been included to calculate pure ARFIMA models with constant variance. the fit method allows the user to input starting parameters as well as keep any parameters from the spec as fixed (including the case of all parameters fixed). Rsolnp While the package has implemented some safeguards. The rmgarch package is still under re-write so the old rgarch package should be used in the meantime for multivariate models (and hosted on r-forge).5).frame” with dates as rownames. “zoo”. These may be added in the future. The conditional distributions used in the package are also exposed for the benefit of the user through the rgarchdist functions which contain methods for density. Explanations on the available methods for the returned classes can be found in the documentation for those classes. Details Package: Type: Version: Date: License: LazyLoad: Depends: rugarch Package 1. fitting ugarchfit. “matrix” and “numeric” vector with dates as names. simulation from fit object ugarchsim. The functionality of the packages is contained in the main methods for defining a specification ugarchspec.00-8 2011-12-16 GPL yes R (>= 2. namely multispec. multifit. both during pre-estimation as well as the estimation phase. distribution. which was split into univariate (rugarch) and multivariate (rmgarch) models for easier maintenance and use. path simulation from specification object ugarchpath. Finally.5).tests folder of the source installation for some tests using ARFIMA models as well as equivalence to the base R arima methods (particularly replication of simulation). Finally. Additionally. multifilter and multiforecast. to the standard ‘alpha-beta-delta-mu’ parametrization of the Generalized Hyperbolic Distribution family. . Journal of Econometrics.H. and Ng. Measuring and Testing the Impact of News on Volatility. Author(s) Alexios Ghalanos References Baillie. Journal of Business and Economic Statistics. Testing density forecasts. Generalized Autoregressive Conditional Heteroskedasticity 1986.rugarch-package 5 the package tries a variety of methods to try to recognize the type and format of the date else will index the data numerically. Engle. Journal of Finance. Berkowitz. Finally. Jagannathan. R. J. note = {R package version 1.O. The ‘inst’ folder of the source distribution also contains various tests which can be sourced and run by the user. please cite as @Manual{Ghalanos_2 11. R. How to cite this package Whenever using this package. K. The user should really consult the examples supplied in this folder which are quite numerous and instructive with some comments. 2001. . 307–327. Fractionally integrated generalized autoregressive conditional heteroskedasticity. 1993. Journal of Econometrics. 1779–1801. 1749–1778. Bollerslev. On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance. V.} License The releases of this package is licensed under GPL version 3. T. Granger.J. 1993. 1. are available through the ugarchbench function.E.W. 48(5). and Bollerslev. year = {2 11}. R. 83–106. A Long Memory Property of Stock Market Returns and a New Model.. R. 3–30 .F. and Mikkelsen. with applications to risk management. and Engle. title = {{rugarch}: Univariate GARCH models.T. Glosten. C. 48. Some benchmarks (published and comparison with commercial package). also exposing some finer details of the functionality of the package.F. 465–474. 31. Journal of Empirical Finance.R.}. 1986.}. Z. Ding.. author = {Alexios Ghalanos}. 19(4). This mostly impacts the plots and forecast summary methods. the user should make use of a non-named representation such as “matrix” or “numeric” as the package has yet to implement methods for checking and working with frequencies higher than daily (and is unlikely to do so). T. 1993. and Runkle. . For high frequency data. The package holds dates internally as class Date. 1996. the functions ForwardDates and WeekDayDummy offer some simple Date manipulation methods for working with forecast dates and creating day of the week dummy variables for use in GARCH modelling. L. D. 351–360. Author(s) Alexios Ghalanos . Romo. L.C. D. 2006. F.B. J. J. 59. Methods No methods defined with class "ARFIMA" in the signature.6 ARFIMA-class Hansen. E. Extends Class "rGARCH". Journal of Financial Economics. Journal of Business and Economic Statistics. B. 1993. Vlaar. Journal of Time Series Analysis.. L. E. ARFIMA-class class: High Level ARFIMA class Description The virtual parent class of the ARFIMA subset. Conditional Heteroskedasticity in Asset Returns: A New Approach. Pascual. 347–370. 1990.J. 1991.E. The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion Conditional Heteroskedasticity and Jumps. Pascual. Langrange Multiplier Tests for Parameter Instability in Non-Linear Models. Bootstrap predictive inference for ARIMA processes. and Palm. Econometrica. 71–104.G. Nelson. Objects from the Class A virtual Class: No objects may be created from it. Computational Statistics and Data Analysis. 2004. and Ruiz. Hentschel. 1995. All in the family Nesting symmetric and asymmetric GARCH models.. mimeo. Ludger. Bootstrap prediction for returns and volatilities in GARCH models. P. 11. 39(1). directly. Romo. and Ruiz. the parameter standard error distribution). objects of which are created by calling function arfimadistribution. model: Object of class "list" The model specification.e. unconditional variance and mean. Class "rGARCH". Author(s) Alexios Ghalanos .e. and “coefse” for the estimated robust standard errors of the coefficients (i.data. Methods as. directly. “stats” for various statistics computed for the simulations such as log likelihood. Slots dist: Object of class "vector" Details of fitted parameters. show signature(object = "ARFIMAdistribution"): parameter distribution summary. namely window which indicates the particular distribution window number for which data is required (is usually just 1 unless the recursive option was used). Extends Class "ARFIMA".data. Valid values for the latter are “rmse” for the root mean squared error between simulation fit and actual parameters. by class "ARFIMA".frame signature(x = "ARFIMAdistribution"): extracts various values from object (see note).frame function takes optionally 2 additional arguments. and which indicating the type of data required. persistence. truecoef: Object of class "matrix" The actual coefficients. “coef” for the estimated coefficients (i. Note The as.ARFIMAdistribution-class 7 ARFIMAdistribution-class class: ARFIMA Parameter Distribution Class Description Class for the ARFIMA Parameter Distribution. distance 2. the parameter distribution and is the default choice). rseed = NA. The burn-in sample. n. The simulation horizon. . fit. Usage arfimadistribution(fitORspec. prereturns preresiduals rseed custom.sim = 2 .start m. parallel. prereturns = NA. recursive. type = "z").pars argument in the specification. custom.sim = 1 . recursive. The number of simulations. . this indicates the final length of the simulation horizon. preresiduals = NA. solver.sim recursive Whether to perform a recursive simulation on an expanding window.length. it determines the total number of separate and increasing length windows which will be simulated and fitted.) Arguments fitORspec Either an ARFIMA fit object of class ARFIMAfit or alternatively an ARFIMA specification object of class ARFIMAspec with valid parameters supplied via the fixed. this must be provided. recursive = FALSE. Optional density with fitted object from which to simulate. with starting length n. Together with recursive. Matrix of simulated external regressor-in-mean data.control = list(). cores = 2)..8 arfimadistribution-methods arfimadistribution-methods function: ARFIMA Parameter Distribution via Simulation Description Method for simulating and estimating the parameter distribution from an ARFIMA models as well as the simulation based consistency of the estimators given the data size. distfit = NA. One of either “nlminb” or “solnp”.dist mexsimdata solver Allows the starting return data to be provided by the user. parallel = FALSE.start = 1. recursive.control Control arguments list passed to optimizer.dist = list(name = NA. n.window If recursive is TRUE. "snowfall"). n.control = list().window = 1 .. solver. this indicates the increment to the expanding window.sim. Allows the starting residuals to be provided by the user. mexsimdata = NULL. If the fit object contains external regressors in the mean equation. m. recursive. Optional seeding value(s) for the random number generator.sim n.length = 6 .length If recursive is TRUE.control = list(pkg = c("multicore". solver = "solnp". 1. ar2= .start = 1 .. as.frame(dist.sim) of the data increases.. window.3.sim = 2 .. 1.model = list(armaOrder = c(2. which=c("rmse".7.arfimadistribution-methods fit. fixed. n. This is an expensive function.frame(dist.pars = list(ar1= . window window window window = = = = 1. m. include.data.frame(dist) as. parallel.21.control Control arguments passed to the fitting routine (as in the arfimafit method). "coefse")) # default as.frame(.mean = TRUE.data.window = 1 ) # slots: slotNames(dist) # methods: # summary show(dist) # as.data. in the sense of the root mean square error (rmse) of the difference between the simulated and true (hypothesized) parameters.. which which which which = = = = "rmse") "stats") "coef") "coefse") .data. both on memory and CPU resources. recursive..data.2). as. 1.sim = 1 . and the number of cores to make use of. ma1=. particularly if using the recursive option. as. mu = . Details This method facilitates the simulation and evaluation of the uncertainty of ARFIMA model parameters. recursive. 2)) dist = arfimadistribution(spec.frame(dist. recursive = TRUE. . "coef". Value A ARFIMAdistribution object containing details of the ARFIMA simulated parameters distribution.6.length = 1 .data.frame(dist. n. sigma = .. distribution. arfima = FALSE).model = "norm". ma2= . 9 parallel Whether to make use of parallel processing on multicore systems. performing many re-fits of the simulated data in order to generate the parameter distribution. 2. Author(s) Alexios Ghalanos Examples ## Not run: spec = arfimaspec( mean.control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S).. The recursive option also allows the evaluation of the simulation based consistency (in terms of sqrt(N) ) of the parameters as the length (n. "stats". . .frame(dist.1 .i-1] = as. ylab = "RMSE Reduction".rmsegr) = c("mu".data.start = as. "ma2".rmsegr[.data.rmsegr = matrix(NA.frame(dist.frame(dist.main = rownames(actual. 8. as. expexcted. xlab = "N (sim)". directly. 8.1 .rmsegr)[i]) lines(seq(3 .by=1 ). nrow = 6) rownames(actual. "ar1". "Expected").3)) for(i in 1:6){ plot(seq(3 . col = 1:2.by=1 )) # actual RMSE reduction actual.start) par(mfrow = c(2. Class "rGARCH". by class "ARFIMA".data. as.10 as. ncol = 8.frame(dist. which = "rmse") for(i in 2:nwindows) actual.data.1 . legend = c("Actual".]. window = i.rmsegr[i. window window window window = = = = 8.actual. as. lty = 2. Slots filter: Object of class "vector" model: Object of class "vector" Extends Class "ARFIMA".frame(dist. distance 2.numeric(as.data. window = 1.data. "ar2". "sigma") # start at 2 (window 1) rmse. "ma2".by=1 ). which = "rmse")/rmse.frame(dist.1)) } ## End(Not run) ARFIMAfilter-class class: ARFIMA Filter Class Description Class for the ARFIMA filter. type = "l". lty = c(2. 8.rmsegr. bty = "m". which which which which = = = = "rmse") "stats") "coef") "coefse") ARFIMAfilter-class # create some plots # nwindows = dist@dist$details$nwindows # 2 /3 /4 /5 /6 /7 /8 /9 /1 # expected reduction factor in RMSE for sqrt(N) consistency expexcted.rmsegr = sqrt(2 /seq(3 . col = 2) legend("topright". pars argument having the model parameters on which the filtering is to take place. matrix. and defaults to 100000) and ‘rseed’ for the simulation random generator initialization seed. data.sample = .. n. Author(s) Alexios Ghalanos Examples showClass("ARFIMAfilter") arfimafilter-methods function: ARFIMA Filtering Description Method for filtering an ARFIMA model. show signature(object = "ARFIMAfilter"): Filter summary. data. infocriteria signature(object = "ARFIMAfilter"): Calculates and returns various information criteria. this is the length of the original dataset (see details). Usage arfimafilter(spec. residuals signature(object = "ARFIMAfilter"): Extracts the residuals.sample n.. . Note that the simulation method is only available for a fitted object or specification with fixed parameters.sim’ for the number of simulations (if that method was chosen. An ARFIMA spec object of class ARFIMAspec with the fixed. xts.) Arguments data spec out. and not for the filtered object.data.arfimafilter-methods Methods 11 as.old .frame signature(x = "ARFIMAfilter"): Extracts the position (dates). timeSeries. coef signature(object = "ARFIMAfilter"): Extracts the coefficients. . likelihood signature(object = "ARFIMAfilter"): Extracts the likelihood.sample argument. .old=NULL.. Takes additional arguments ‘method’ with option for “analytical” or “simulation”. data. filtered values and residuals. A univariate data object. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (as in arfimafit function). zoo. ts or irts object. ‘n. out. For comparison with ARFIMA models using the out. Can be a numeric vector. uncmean signature(object = "ARFIMAfilter"): Calculates and returns the unconditional mean. fitted signature(object = "ARFIMAfilter"): Extracts the filtered values.frame.. "sged".control = list(scale = 1)) } cfmatrix = matrix(NA. hq) colnames(cfmatrix)=c(colnames(cfmatrix[. skew = cf["skew"]. distribution. "skewness". "skew". The reason for using this is so that the old and new datasets agree since the original recursion uses the sum of the residuals to start the recursion and therefore is influenced by new data. length = 9) .kurtosis".12 Details arfimafilter-methods The n. 9) for(i in 1:9){ cf = coef(fit[[i]]) if(fit[[i]]@model$modelinc[16]> ) sk[i] = dskewness(distribution = dist[i]. ncol = 7) colnames(cfmatrix) = c("mu". "sstd". "ghlambda") rownames(cfmatrix) = dist for(i in 1:9){ cf = coef(fit[[i]]) cfmatrix[i. include. For a small augmentation the values converge after x periods. shape = cf["shape"]. data = sp5 ret. "ma1". length = 9) dist = c("norm". arfima = FALSE). FUN = function(x) infocriteria(x)[4]) cfmatrix = cbind(cfmatrix. lambda = cf["ghlambda"]) if(fit[[i]]@model$modelinc[17]> ) ku[i] = dkurtosis(distribution = dist[i]. "nig". solver = "solnp". shape = cf["shape"].1:7]). "ar1".old argument is optional and indicates the length of the original data (in cases when this represents a dataseries augmented by newer data). "snorm"."HQIC") # filter the data to check results filt = vector(mode = "list". Author(s) Alexios Ghalanos Examples ## Not run: data(sp5 ret) fit = vector(mode = "list".model = dist[i]) fit[[i]] = arfimafit(spec = spec. "jsu") for(i in 1:9){ spec = arfimaspec(mean.1). lambda = cf["ghlambda"]) } hq = sapply(fit. skew = cf["skew"]. but it is sometimes preferable to have this option so that there is no forward looking information contaminating the study. match(names(cf).mean = TRUE. colnames(cfmatrix))] = cf } sk = ku = rep( . ku. "ged". Value A ARFIMAfilter object containing details of the ARFIMA filter. nrow = 9.model = list(armaOrder = c(1. "sigma". "shape". "ghyp". "std". sk. "ex. fit. n. head(fitted(fit[[1]])))) cat("\ninfocriteria method:\n") # For filter.data.frame(filt[[1]])). arfima = FALSE).mean = TRUE.model = dist[1]) setfixed(spec) = as.frame(fit[[1]])))) cat("\ncoef method:\n") print(cbind(coef(filt[[1]]). FUN = function(x) residuals(x)))) cat("\nas. distribution.sim = 1 . rseed = 1 ))) cat("\nsummary method:\n") show(filt[[1]]) show(fit[[1]]) ## End(Not run) 13 ARFIMAfit-class class: ARFIMA Fit Class Description Class for the ARFIMA fit.data.e. uncmean(fit[[1]]))) cat("\nuncmean method (by simulation):\n") # For spec and fit spec = arfimaspec( mean. likelihood(fit[[1]]))) cat("\nresiduals method:\n") # Note that we the package will always return the full length residuals and # fitted object irrespective of the lags (i. n.list(coef(fit[[i]])) filt[[i]] = arfimafilter(spec = spec. since this is an ARMA(1.frame method:\n") print(cbind(head(as. head(as. arfima = FALSE).data. uncmean(fit[[1]].1).mean = TRUE. print(cbind(head(residuals(filt[[1]])). method = "simulation".model = list(armaOrder = c(1. include. infocriteria(fit[[1]]))) cat("\nlikelihood method:\n") print(cbind(likelihood(filt[[1]]). coef(fit[[1]]))) cat("\nfitted method:\n") print(cbind(head(fitted(filt[[1]])). Slots fit: Object of class "vector" . distribution. the first row is zero and should be discarded.ARFIMAfit-class for(i in 1:9){ spec = arfimaspec(mean.1).model = dist[i]) setfixed(spec) = as.list(coef(fit[[1]])) print(cbind(uncmean(spec. method = "simulation".e.sim = 1 . FUN = function(x) residuals(x))) == head(sapply(fit. digits = 4) cat("\nARFIMAfit and ARFIMAfilter residuals check:\n") print(head(sapply(filt. rseed = 1 ).1) # i. it assumes estimation of parameters else does not make sense! print(cbind(infocriteria(filt[[1]]).model = list(armaOrder = c(1. max lag = 1. data = sp5 ret) } print(cfmatrix. head(residuals(fit[[1]])))) cat("\nuncmean method:\n") print(cbind(uncmean(filt[[1]]). include. data.se = .control = list(fixed. show signature(object = "ARFIMAfit"): Fit summary. Methods arfimafit-methods as. Author(s) Alexios Ghalanos Examples showClass("ARFIMAfit") arfimafit-methods function: ARFIMA Fit Description Method for fitting an ARFIMA models. Takes additional arguments ‘method’ with option for “analytical” or “simulation”. ‘n.control = list(). solver = "solnp".sample = .14 model: Object of class "vector" Extends Class "ARFIMA". likelihood signature(object = "ARFIMAfit"): Extracts the likelihood.frame signature(x = "ARFIMAfit"): Extracts the position (dates). and defaults to 100000) and ‘rseed’ for the simulation random generator initialization seed. infocriteria signature(object = "ARFIMAfit"): Calculates and returns various information criteria.) . out. coef signature(object = "ARFIMAfit"): Extracts the coefficients... data. . by class "ARFIMA". directly. uncmean signature(object = "ARFIMAfit"): Calculates and returns the unconditional mean. solver. Usage arfimafit(spec. residuals signature(object = "ARFIMAfit"): Extracts the residuals. fit. data. fitted signature(object = "ARFIMAfit"): Extracts the fitted values. Class "rGARCH".sim’ for the number of simulations (if that method was chosen. scale = ). fitted values and residuals. distance 2. sample points for forecasting and testing using the forecast performance measures. xts. The out. An ARFIMA spec object of class ARFIMAspec.out. “rseed” is the seed to initialize the random number generator. data.pars argument of the arfimaspec function)..control” for use of the parallel functionality.sample solver fit. timeSeries.sample (where N is the total data length) data points. In the arfimaforecast routine the n.control Control arguments list passed to optimizer.sample option is provided in order to carry out forecast performance testing against actual data. Author(s) Alexios Ghalanos Examples ## Not run: data(sp5 ret) fit = vector(mode = "list". solver. . The solver. The fixed. “parallel” and “parallel.arfimafit-methods Arguments data spec out. which the forecast performance tests will ignore. then the routine will fit only N . If the out. Value A ARFIMAfit object containing details of the ARFIMA fit. matrix. ts or irts object.. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (see details).ahead may also be greater than the out.se argument controls whether standard errors should be calculated for those parameters which were fixed (through the fixed.sample option is positive. Can be a numeric vector. “solnp” or “gosolnp”. The scale parameter controls whether the data should be scaled before being submitted to the optimizer.restarts.control list then accepts the following additional (to the solnp) arguments: “n. The main part of the likelihood calculation is performed in C-code for speed. and “n. One of either “nlminb”.frame. A minimum of 5 data points are required for these tests. leaving out. Control arguments passed to the fitting routine. The “gosolnp” solver allows for the initialization of multiple restarts of the solnp solver with randomly generated parameters (see documentation in the Rsolnp-package for details of the strategy used).restarts” is the number of solver restarts required (defaults to 1).sim” is the number of simulated parameter vectors to generate per n. Details The ARFIMA optimization routine first calculates a set of feasible starting points which are used to initiate the ARFIMA Maximum Likelihood recursion.control 15 A univariate data object. zoo. . length = 9) .sample number resulting in a combination of out of sample data points matched against actual data and some without. "ex. "sstd". "ged". ku. 9) for(i in 1:9){ cf = coef(fit[[i]]) if(fit[[i]]@model$modelinc[16]> ) sk[i] = dskewness(distribution = dist[i]. the first row is zero and should be discarded). method = "simulation". match(names(cf). nrow = 9.model = dist[i]) fit[[i]] = arfimafit(spec = spec. since this is an ARMA(1.16 arfimafit-methods dist = c("norm". sk. rseed = 1 ) cat("\nsummary method:\n") show(fit[[1]]) ## End(Not run) . "ghyp". skew = cf["skew"].data. cat("\nas. "sged". head(residuals(fit[[1]])) cat("\nuncmean method:\n") uncmean(fit[[1]]) cat("\nuncmean method (by simulation):\n") uncmean(fit[[1]].1) # i.e. distribution.model = list(armaOrder = c(1."HQIC") print(cfmatrix.1). "skewness".1:7]). fit.control = list(scale = 1)) } cfmatrix = matrix(NA. hq) colnames(cfmatrix)=c(colnames(cfmatrix[. shape = cf["shape"]. digits = 4) # notice that for the student distribution kurtosis is NA since shape (dof) < 4. n. include. lambda = cf["ghlambda"]) if(fit[[i]]@model$modelinc[17]> ) ku[i] = dkurtosis(distribution = dist[i].frame method:\n") head(as. data = sp5 ret.e.frame(fit[[1]])) cat("\ncoef method:\n") coef(fit[[1]]) cat("\nfitted method:\n") head(fitted(fit[[1]])) cat("\ninfocriteria method:\n") infocriteria(fit[[1]]) cat("\nlikelihood method:\n") likelihood(fit[[1]]) cat("\nresiduals method:\n") # Note that we the package will always return the full length residuals and # fitted object irrespective of the lags (i.sim = 1 . "shape". "jsu") for(i in 1:9){ spec = arfimaspec(mean. "snorm". "skew". solver = "solnp". colnames(cfmatrix))] = cf } sk = ku = rep( . "ar1".mean = TRUE. FUN = function(x) infocriteria(x)[4]) cfmatrix = cbind(cfmatrix. "sigma". ncol = 7) colnames(cfmatrix) = c("mu". "nig". max lag = 1.kurtosis". "std". skew = cf["skew"]. lambda = cf["ghlambda"]) } hq = sapply(fit. "ghlambda") rownames(cfmatrix) = dist for(i in 1:9){ cf = coef(fit[[i]]) cfmatrix[i. "ma1".data. shape = cf["shape"]. arfima = FALSE). Finally.data.frame method on the other hand provides for 4 additional arguments. the data. Slots forecast: Object of class "vector" model: Object of class "vector" Extends Class "ARFIMA". some or all these options may be useful to the user when extracting data from the forecast object.frame returned may be time aligned (logical option aligned) in which case the logical option prepad indicates whether to pad the values prior to the forecast start time with actual values or NA (value FALSE). show signature(object = "ARFIMAforecast"): Forecast summary returning the 0-roll frame only. . directly. The as. by class "ARFIMA".frame signature(x = "ARFIMAforecast"): Extracts the forecasts. Class "rGARCH". the type option controls whether to return all forecasts (value 0. The rollframe option is for the rolling frame to return (with 0 being the default no-roll) and allows either a valid numeric value or alternatively the character value “all” for which additional options then come into play. return only those forecasts which have in sample equivalent data (value 1) or return only those values which are truly forecasts without in sample data (value 2). There are no additional arguments to these extractor functions and they will return all the forecasts.ahead value and row dimension 1 (series forecast). as. Methods as.ARFIMAforecast-class 17 ARFIMAforecast-class class: ARFIMA Forecast Class Description Class for the ARFIMA forecast. The as. Note There are 3 main extractor functions for the ARFIMA object which is admittedly the most complex in the package as a result of allowing for rolling forecasts. and array dimension equal to the number of rolling forecasts chosen.list signature(x = "ARFIMAforecast"): Extracts the forecast list with all rollframes. Takes many additional arguments (see note below).data. distance 2.list method works similarly returns instead a list object. fpm signature(object = "ARFIMAforecast"): Forecast performance measures.array extracts an array object where each page of the array represents a roll.array signature(x = "ARFIMAforecast"): Extracts the forecast array with matrix column dimensions equal to the n. When “all” is chosen in the rollframe argument. The as. default). as. Depending on the intended usage of the forecasts. One step ahead forecasts are based on the value of the previous data. out.ahead = 1 . n.roll argument.forecasts = list(mregfor = NULL). the out. If a specification object is supplied. of rolling forecasts to create beyond the first one (see details). .sample argument directly in the forecast function.. data = NULL.sample Optional. or a specification object (in which case the data is required) with the parameters entered via the set.) Arguments fitORspec Either an ARFIMA fit object of class ARFIMAfit or alternatively an ARFIMA specification object of class ARFIMAspec with valid parameters supplied via the fixed.. external.roll argument which controls how many times to roll the n.forecasts A list with a matrix of forecasts for the external regressors in the mean. .roll = .sample = . The no. n. The ability to roll the forecast 1 step at a time is implemented with the n. data n.roll out. while n-step ahead (n>1) are based on the unconditional mean of the model. or in the case of a specification being used instead of a fit object.fixed<. Required if a specification rather than a fit object is supplied. Critically. ..methods on an ARFIMAspec object. indicates how many data points to keep for out of sample testing. Details The forecast function has two dispatch methods allowing the user to call it with either a fitted object (in which case the data argument is ignored).ahead forecast.roll depends on data being available from which to base the rolling forecast. since n.pars argument in the specification.sample being at least as large as the n. Usage arfimaforecast(fitORspec.ahead n. external. . the arfimafit function needs to be called with the argument out.ahead forecast. The default argument of n..roll = 0 denotes no rolling beyond the first forecast and returns the standard n.18 Author(s) Alexios Ghalanos arfimaforecast-methods arfimaforecast-methods function: ARFIMA Forecasting Description Method for forecasting from an ARFIMA model. The forecast horizon. model = dist[i]) setfixed(spec) = as. "sigma".mean = TRUE. "nig".1). data = sp5 ret. "ar1". "snorm".control = list(scale = 1)) } cfmatrix = matrix(NA.numeric(as. distribution. length = 9) for(i in 1:9){ forc[[i]] = arfimaforecast(fit[[i]]. "ged". data = sp5 ret. "sged".1:7]). Author(s) Alexios Ghalanos Examples ## Not run: # Long Horizon Forecast data(sp5 ret) fit = vector(mode = "list".model = list(armaOrder = c(1. arfima = FALSE). solver = "solnp". include.1).arfimaforecast-methods Value 19 A ARFIMAforecast object containing details of the ARFIMA forecast. "forecast4 ") # forecast with spec to check results forc2 = vector(mode = "list". distribution.frame(x)[4 . umean. "ma1".model = dist[i]) fit[[i]] = arfimafit(spec = spec. colnames(cfmatrix))] = } umean = rep( . "ghlambda") rownames(cfmatrix) = dist for(i in 1:9){ cf = coef(fit[[i]]) cfmatrix[i. arfima = FALSE). length = 9) dist = c("norm".ahead = 1 ) } . ncol = 7) colnames(cfmatrix) = c("mu". n. n. "std". FUN = function(x) as. length = 9) for(i in 1:9){ spec = arfimaspec(mean. match(names(cf).list(coef(fit[[i]])) forc2[[i]] = arfimaforecast(spec.1])) cfmatrix1 = cbind(cfmatrix. "ghyp". nrow = 9. include.mean = TRUE. lmean4 ) colnames(cfmatrix1) = c(colnames(cfmatrix1[.ahead = 1 } cf ) lmean4 = sapply(forc. "sstd". See the class for details on the returned object and methods for accessing it and performing some tests. "skew". "shape". fit. 9) for(i in 1:9){ umean[i] = uncmean(fit[[i]]) } forc = vector(mode = "list".data. "jsu") for(i in 1:9){ spec = arfimaspec(mean. "uncmean".model = list(armaOrder = c(1. "nig". "skew".roll = 999) } rollforc = sapply(forc. nrow = 9.frame as.numeric(as. length = 9) for(i in 1:9){ . "shape".sample = 1 . rollframe = "all".ahead = 1.frame(forc[[1]]) # as. no rolling beyond # the first) as. umean.frame(x. digits = 4) cat("\nSpec\n") print(cfmatrix2. distribution. out.e.1:7]). "ar1". "ged". length = 9) for(i in 1:9){ forc[[i]] = arfimaforecast(fit[[i]]. length = 9) dist = c("norm". FUN = function(x) t(unlist(as. n.1). "sigma".control = list(scale = 1)) } cfmatrix = matrix(NA. "ghlambda") rownames(cfmatrix) = dist for(i in 1:9){ cf = coef(fit[[i]]) cfmatrix[i.model = dist[i]) fit[[i]] = arfimafit(spec = spec. "ghyp". FUN = function(x) as.model = list(armaOrder = c(1.data.list as.1])) cfmatrix2 = cbind(cfmatrix. n. digits = 4) # methods and slots slotNames(forc[[1]]) showMethods(classes="ARFIMAforecast") # summary show(forc[[1]]) # Extractor Functions # as array (array dimension [3] is 1 since n. match(names(cf). fit. solver = "solnp". "forecast4 ") cat("\nARFIMAforecast from ARFIMAfit and ARFIMAspec check:") cat("\nFit\n") print(cfmatrix1.roll = i. lmean24 ) colnames(cfmatrix2) = c(colnames(cfmatrix2[. "uncmean". "ma1". arfima = FALSE). data = sp5 ret.20 arfimaforecast-methods lmean24 = sapply(forc2. include. "sstd".data.mean = TRUE. "jsu") for(i in 1:9){ spec = arfimaspec(mean. colnames(cfmatrix))] = } cf forc = vector(mode = "list". "std". "snorm". "sged".data.list(forc[[1]]) # Rolling Forecast data(sp5 ret) fit = vector(mode = "list". aligned = FALSE)))) # forecast performance measures: fpmlist = vector(mode = "list".data.array(forc[[1]]) # as.frame(x)[4 . ncol = 7) colnames(cfmatrix) = c("mu". ylim = c(. col = clrs. names = dist. summary = TRUE) show(forc[[1]]) ## End(Not run) 21 ARFIMAmultifilter-class class: ARFIMA Multiple Filter Class Description Class for the ARFIMA Multiple filter.i] lines(as. main = "Rolling 1-ahead Forecasts\nAbsolute Deviation Loss") # fpm comparison compm = matrix(NA.2)) dd = rownames(tail(sp5 ret. . "DAC") cat("\nRolling Forecast FPM\n") print(compm. nrow = 3. tmp[-(1:25 )]). start = ."SE"]).1]. 125 ). aligned = FALSE)) fpm(forc[[1]].frame(forc[[1]]. 2). main = "Rolling 1-ahead Forecasts\nvs Actual") for(i in 1:9){ tmp = tail(sp5 ret[."AE"] names(tmp[[i]]) = dist[i] } boxplot(tmp.4.data. "MAD". rollframe = "all". fill = clrs. digits = 4) cat("\nMethods Check\n") as.Date(dd).ARFIMAmultifilter-class fpmlist[[i]] = fpm(forc[[i]]. type = "l". . mean(x[. FUN = function(x) c(mean(x[. 125 )) clrs = rainbow(9. range = 6. alpha = 1. legend = dist.data. 125 ) tmp[251:125 ] = rollforc[1:1 . col = clrs. c(rep(NA. mean(x[. col = "lightgrey". 2. rollframe = 999) t(as.95) plot(as. length = 9) for(i in 1:9){ tmp[[i]] = fpmlist[[i]][."AE"]). col = clrs[i]) } legend("topleft". ncol = 9) compm = sapply(fpmlist. ylab = ""."DAC"]))) colnames(compm) = dist rownames(compm) = c("MSE". end = . rollframe = ) as. 25 ).frame(forc[[1]]. bty = "n") # plot deviation measures and range tmp = vector(mode = "list".Date(dd).1].data.. notch = TRUE.frame(forc[[1]]. xlab = "". summary = FALSE) } par(mfrow = c(1. tail(sp5 ret[. 22 Slots filter: Object of class "vector" desc: Object of class "vector" Extends Class "ARFIMA". show signature(object = "ARFIMAmultifilter"): filter summary. likelihood signature(object = "ARFIMAmultifit"): extracts the likelihood. distance 2. residuals signature(object = "ARFIMAmultifilter"): extracts the residuals. likelihood signature(object = "ARFIMAmultifilter"): extracts the likelihood. Slots fit: Object of class "vector" desc: Object of class "vector" Extends Class "ARFIMA". directly. directly. Author(s) Alexios Ghalanos . Methods ARFIMAmultifit-class fitted signature(object = "ARFIMAmultifilter"): extracts the fitted values. Class "rGARCH". by class "ARFIMA". Author(s) Alexios Ghalanos ARFIMAmultifit-class class: ARFIMA Multiple Fit Class Description Class for the ARFIMA Multiple fit. residuals signature(object = "ARFIMAmultifit"): extracts the residuals. Class "rGARCH". distance 2. fitted signature(object = "ARFIMAmultifit"): extracts the fitted values. coef signature(object = "ARFIMAmultifilter"): extracts the coefficients. show signature(object = "ARFIMAmultifit"): fit summary. by class "ARFIMA". Methods coef signature(object = "ARFIMAmultifit"): extracts the coefficients. roll. Author(s) Alexios Ghalanos ARFIMAmultispec-class class: ARFIMA Multiple Specification Class Description Class for the ARFIMA Multiple specification.ARFIMAmultiforecast-class 23 ARFIMAmultiforecast-class class: ARFIMA Multiple Forecast Class Description Class for the ARFIMA Multiple forecast. as. sublists equal to n. distance 2.list signature(x = "ARFIMAmultiforecast"): extracts the forecast list of length equal to the number of assets. Slots forecast: Object of class "vector" desc: Object of class "vector" Extends Class "ARFIMA". by class "ARFIMA". directly. Class "rGARCH". row dimension of each sublist equal to n. Methods as. Slots spec: Object of class "vector" type: Object of class "character" . row dimension the n.ahead and column dimension equal to 1 (series forecasts).array signature(x = "ARFIMAmultiforecast"): extracts the forecast array with matrix column dimensions equal to the number of assets.ahead and array dimension equal to the number of rolling forecasts chosen. show signature(object = "ARFIMAmultiforecast"): forecast summary. frame function takes optionally 1 additional arguments. Methods show signature(object = "ARFIMAmultispec"): specification summary. Note The as.frame will be n. directly. Class "rGARCH". Slots path: Object of class "vector" model: Object of class "vector" seed: Object of class "integer" Extends Class "ARFIMA". indicating the type of simulation path series to extract. Class "rGARCH".data.sim by m.frame signature(x = "ARFIMApath"): Extracts the simulated path values (see note). by class "ARFIMA". directly. Author(s) Alexios Ghalanos .data. The dimension of the data.24 Extends Class "ARFIMA". show signature(object = "ARFIMApath"): path simulation summary. Author(s) Alexios Ghalanos ARFIMApath-class ARFIMApath-class class: ARFIMA Path Simulation Class Description Class for the ARFIMA Path simulation. distance 2. by class "ARFIMA".sim. Valid values “series” for the simulated series and “residuals” for the simulated residuals. namely which. distance 2. Methods as. mexsimdata=NULL. preresiduals = NA. The burn-in sample.dist=list(name = NA. . The “type” argument denotes whether the standardized innovations are passed (“z”) else the innovations (anything other than “z”). type = "z"). Allows the starting return data to be provided by the user. Instead.arfimapath-methods 25 arfimapath-methods function: ARFIMA Path Simulation Description Method for simulating the path of an ARFIMA model. Usage arfimapath(spec. . Allows the starting residuals to be provided by the user.argument to the spec.pars list argument.start m.sim prereturns preresiduals rseed custom. This is a convenience function which does not require a fitted object (see note below)..sim = 1.. n. The simulation horizon.. distfit = NA. Matrix of simulated external regressor-in-mean data. Optional density with fitted object from which to simulate.sim = 1 . rseed = NA.) Arguments spec n. prereturns = NA. Optional seeding value(s) for the random number generator. an arfima spec object is required with the model parameters supplied via the setfixed<. The number of simulations. If the fit object contains external regressors in the mean equation. custom.start = .sim n. Details This is a convenience method to allow path simulation of ARFIMA models without the need to supply a fit object as in the arfimasim method. Author(s) Alexios Ghalanos . n.dist An ARFIMA object of class ARFIMAspec with the required parameters of the model supplied via the fixed. this must be provided.. Value A ARFIMApath object containing details of the ARFIMA path simulation. mexsimdata . m. 26 ARFIMAroll-class ARFIMAroll-class class: ARFIMA Rolling Forecast Class Description Class for the ARFIMA rolling forecast. Slots roll: Object of class "vector" forecast: Object of class "vector" model: Object of class "vector" Extends Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2. Methods as.ARFIMAforecast signature(object = "ARFIMAroll"): extracts and converts the forecast object contained in the roll object to one of ARFIMAforecast given the refit number supplied by additional argument ‘refit’ (defaults to 1). as.data.frame signature(x = "ARFIMAroll"): extracts various values from object (see note). fpm signature(object = "ARFIMAroll"): Forecast performance measures. report signature(object = "ARFIMAroll"): roll backtest reports (see note). Note The as.data.frame extractor method allows the extraction of a variety of values from the object. Additional arguments are: which indicates the type of value to return. Valid values are “coefs” returning the parameter coefficients for all refits, “density” for the parametric density, “coefmat” for the parameter coefficients with their respective standard errors and t- and p- values, “LLH” for the likelihood across the refits, and “VaR” for the Value At Risk measure if it was requested in the roll function call. n.ahead for the n.ahead forecast horizon to return if which was used with arguments “density” or ‘VaR’. refit indicates which refit window to return the “coefmat” if that is chosen. If “series” is chosen under via the which argument, then the forecast series is returned for a particular refit, else when “all” is used it returns the complete forecasted series across all refits. The report method takes the following additional arguments: type for the report type. Valid values are “VaR” for the Value at Risk report based on the unconditional and conditional coverage tests for VaR exceedances (discussed below) and “fpm” for forecast performance measures. n.ahead for the rolling n.ahead forecasts (defaults to 1). VaR.alpha for the Value at Risk backtest report, this is the tail probability and defaults to 0.01. conf.level the confidence level upon which the conditional coverage hypothesis test will be based arfimaroll-methods 27 on (defaults to 0.95). Kupiec’s unconditional coverage test looks at whether the amount of expected versus actual exceedances given the tail probability of VaR actually occur as predicted, while the conditional coverage test of Christoffersen is a joint test of the unconditional coverage and the independence of the exceedances. Both the joint and the separate unconditional test are reported since it is always possible that the joint test passes while failing either the independence or unconditional coverage test. The “fpm” does not take any additional arguments, but instead returns the forecast performance measures for all “n.ahead” values. Author(s) Alexios Ghalanos arfimaroll-methods function: ARFIMA Rolling Density Forecast and Backtesting Description Method for creating rolling density forecast from ARFIMA models with option for refitting every n periods and some multicore parallel functionality. Usage arfimaroll(spec, data, n.ahead = 1, forecast.length = 5 , refit.every = 25, refit.window = c("recursive", "moving"), parallel = FALSE, parallel.control = list(pkg = c("multicore", "snowfall"), cores = 2), solver = "solnp", fit.control = list(), solver.control = list(), calculate.VaR = TRUE, VaR.alpha = c( . 1, . 5), ...) Arguments spec data An ARFIMA spec object specifiying the desired model for testing. A univariate dataset. n.ahead The number of periods to forecast. forecast.length The length of the total forecast for which out of sample data from the dataset will be excluded for testing. refit.every refit.window Determines every how many periods the model is re-estimated. Whether the refit is done on an expanding window including all the previous data or a moving window, the length of the window determined by the argument above (refit.every). Whether to make use of parallel processing on multicore systems. parallel 28 arfimaroll-methods parallel.control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S), and the number of cores to make use of. solver fit.control The solver to use. Control parameters parameters passed to the fitting function. solver.control Control parameters passed to the solver. calculate.VaR VaR.alpha ... Whether to calculate forecast Value at Risk during the estimation. The Value at Risk tail level to calculate. . Details ARFIMA models generate a partially time varying density based on the variation in the conditional mean values (sigma, skewness and shape are not time varying). The function first generates rolling forecasts of the ARFIMA model and then rescales the density from a standardized (0, 1, skew, shape) to the one representing the underlying return process (mu, sigma, skew, shape). Given this information it is then a simple matter to generate any measure of risk through the analytical evaluation of some type of function of the density. The function calculates one such measure (VaR), but since the full density parameters are returned, the user can calculate many others. The argument refit.every determines every how many periods the fit is recalculated and the total forecast length actually calculated. For example, for a forecast length of 500 and refit.every of 25, this is 20 windows of 25 periods each for a total actual forecast length of 500. However, for a refit.every of 30, we take the floor of the division of 500 by 30 which is 16 windows of 30 periods each for a total actual forecast length of 480 (16 x 30). The important thing to remember about the refit.every is that it acts like the n.roll argument in the arfimaforecast function as it determines the number of rolls to perform. For example for n.ahead of 1 and refit.every of 25, the forecast is rolled every day using the filtered (actual) data of the previous period while for n.ahead of 1 and refit.every of 1 we will get 1 n.ahead forecasts for every day after which the model is refitted and reforecast for a total of 500 refits (when length.forecast is 500)! Value An object of class ARFIMAroll. Author(s) Alexios Ghalanos data.) . show signature(object = "ARFIMAsim"): simulation summary.sim by m. "sample").frame function takes optionally 1 additional arguments.data. n.. startMethod = c("unconditional". directly. n. The dimension of the data.sim = 1 . distfit = NA. Valid values are “series” for the simulated series and “residuals” for the simulated residuals.ARFIMAsim-class 29 ARFIMAsim-class class: ARFIMA Simulation Class Description Class for the ARFIMA simulation.start = .dist = list(name = NA. Author(s) Alexios Ghalanos arfimasim-methods function: ARFIMA Simulation Description Method for simulation from ARFIMA models. by class "ARFIMA". distance 2. custom. namely which. Methods as.. indicating the type of simulation series to extract.frame will be n.sim. . prereturns = NA. Usage arfimasim(fit. preresiduals = NA.frame signature(x = "ARFIMAsim"): extracts the simulated values (see note). m. Class "rGARCH". Slots simulation: Object of class "vector" model: Object of class "vector" seed: Object of class "integer" Extends Class "ARFIMA". rseed = NA. mexsimdata = NULL.sim = 1. Note The as. type = "z"). See notes below for details.sim startMethod prereturns preresiduals rseed custom. Optional density with fitted object from which to simulate. The number of simulations.30 Arguments fit n.g.start m.g. this can be provided else will be ignored.dist can take any name in the name slot (e. dnorm). The simulation horizon. Slots model: Object of class "vector" . The burn-in sample. e.sim n. Value A ARFIMAsim object containing details of the ARFIMA simulation. Alternatively. rnorm) and “d” (density e.sim (rows). Details The custom.sim (columns) and n.g. Starting values for the simulation. Allows the starting return data to be provided by the user. It must take a single fit object as its second argument. mexsimdata .“sample”) and a matrix in the fit slot with dimensions equal to m. The “type” argument denotes whether the standardized innovations are passed (“z”) else the innovations (anything other than “z”). Allows the starting residuals to be provided by the user. If the fit object contains external regressors in the mean equation.dist An ARFIMA fit object of class ARFIMAfit. ARFIMAspec-class Optional seeding value(s) for the random number generator. Matrix of simulated external regressor-in-mean data..dist option allows for defining a custom density which exists in the users workspace with methods for “r” (sampling. . Author(s) Alexios Ghalanos ARFIMAspec-class class: ARFIMA Specification Class Description Class for the ARFIMA specification. custom.. 31 setfixed<. directly. “nig” for the normal inverse gaussian distribution.arfimaspec-methods Extends Class "ARFIMA".model .mean = TRUE. “ged” for the generalized error distribution. distribution. value = "vector"): Sets the fixed parameters (which must be supplied as a named list). Valid choices are “norm” for the normal distibution. include. . start..mean Whether to include the mean. Methods show signature(object = "ARFIMAspec"): Specification summary. fixed. Note that some of the distributions are taken mean. “std” for the student-t. 1). distribution. arfima = FALSE. “ghyp” for the Generalized Hyperbolic. Author(s) Alexios Ghalanos arfimaspec-methods function: ARFIMA Specification Description Method for creating an ARFIMA specification object prior to fitting.regressors A matrix object containing the external regressors to include in the mean equation with as many rows as will be included in the data (which is passed in the fit function). value = "vector"): Sets the starting parameters (which must be supplied as a named list). Usage arfimaspec(mean.model The distribution density to use for the innovations.model = "norm". “snorm” for the skew-normal distribution..pars = list().signature(object = "ARFIMAspec". arfima Whether to include arfima. external. and “jsu” for Johnson’s SU distribution.regressors = NULL).signature(object = "ARFIMAspec". include. distance 2. by class "ARFIMA". uncmean signature(object = "ARFIMAspec"): Returns the unconditional mean of a specification which has been assigned fixed parameters. “sstd” for the skew-student-t. setstart<. Class "rGARCH".pars = list(). “sged” for the skew-generalized error distribution.) Arguments List containing the mean model specification: armaOrder The autoregressive (ar) and moving average (ma) orders (if any). external.model = list(armaOrder = c(1. the list below exposes the names used for the parameters:(note that when a parameter is followed by a number. this represents the order of the model. Details The specification allows for flexibility in ARFIMA modelling. The optional argument “fixed. . Just increment the number for higher orders): Mean Model: constant AR term MA term exogenous regressors arfima mu ar1 ma1 mxreg1 darfima Distribution Model: dlambda skew shape dlambda (for GHYP distribution) skew shape Value A ARFIMAspec object containing details of the ARFIMA specification.32 arfimaspec-methods from the fBasics package and implenented locally here for convenience. start. In order to understand which parameters can be entered in the start. These are not usually required unless the optimization has problems converging. List of parameters which are to be kept fixed during the optimization.pars and fixed.. It is possible that you designate all parameters as fixed so as to quickly recover just the results of some previous work or published work. .pars fixed.pars optional arguments.. Author(s) Alexios Ghalanos .se” in the arfimafit function indicates whether to calculate standard errors for those parameters fixed during the post optimization stage. The “jsu” distribution is the reparametrized version from the “gamlss” package.pars List of staring parameters for the optimization routine. unit variance and zero coefficients in the autoregressive lags. 5.test = FALSE. The restricted Log-Likelihood with zero mean. Usage BerkowitzLR(data. The estimated autoregressive coefficients of the model (not calculated when tail. The LR test statistic p-value (distributed chisq with 2+lags d.f). Value A list with the following items: uLL rLL LR LRp H Test mu sigma rho JB JBp The unconditional Log-Likelihood of the maximized values. . A univariate vector of standard normal transformed values (see details and example).BerkowitzLR 33 BerkowitzLR Berkowitz Density Forecast Likelihood Ratio Test Description Implements the Berkowitz Density Forecast Likelihood Ratio Test. lags = 1. The number of autoregressive lags (positive and greater than 0).test alpha Details See not below. tail. The Likelihood Ratio Test Statistic.test is used). significance = . The estimated mean of the model. The Jarque-Bera Test of Normality Statistic (not calculated when tail. alpha = .test is used).test is used). The test of the Null Hypothesis at the requested level of significance. The estimated sd of the model. The Jarque-Beta Test Statistic p-value (not calculated when tail.test cuttoff. 5) Arguments data lags significance tail. The quantile level for the tail. The Null Hypothesis.o. The level of significance at which the Null Hypothesis is evaluated. Whether to use the tail test of Berkowitz using a censored likelihood. frame(pred. variance.1]. 2001. 1952. drop = FALSE]. include. transform the actual(observed) realizations of the data by applying the distribution function of the forecast density (p*). data(dji3 ret) spec = ugarchspec(mean.test is used.array(pred)[.dmatrix). skew = x[4]. with applications to risk management.1. Rosenblatt.].as. rollframe = 999) tail(dji3 ret[. n. Given a forecast density (d*) at time t. This will result in a set of uniform values (see Rosenblatt (1952)).1. 17(4). RISK Magazine. drop = FALSE]. distribution. Jarque. 86–87. Remarks on a multivariate transformation. "sigma". coef(fit)["skew"].1).data.ahead = 1. K. 1.array(pred)[. Journal of Business and Economic Statistics.2. 1 ) # you can check that this is correct by looking at the dates of the first and # last predictions: as.roll = 999) dmatrix = cbind(as. drop = FALSE]. 470–472. 1.K. 1987m A test for normality of observations and regression residuals. C. International Statistical Review.frame(pred.M. Author(s) Alexios Ghalanos References Berkowitz. 465–474. A modified Berkowitz back-test. A. The Annals of Mathematical Statistics.].1. FUN = function(x) pdist("nig". J. The function also returns the Jarque Bera Normality Test statistic as an additional check of the normality assumption which the test does not explicitly account for (see Dowd reference).data. The example below hopefully clarifies this.34 Note BerkowitzLR The data must first be transformed before being submitted to the function as described here.model = list(armaOrder = c(6. 1) as. 163–172. When tail. Transform those value into standard normal variates by applying the standard normal quantile function (qnorm). Examples ## Not run: # A univariate GARCH model is used with rolling out of sample forecasts. 19(4). sigma = x[3]. Testing density forecasts. "shape") # Get Realized (Oberved) Data obsx = tail(dji3 ret[.mean = TRUE). q = x[1]. shape = x[5])) . out.sample = 1 ) pred = ugarchforecast(fit. Dowd. 1 ).model = list(model = "gjrGARCH"). n. 2004. "skew". 1) # Transform to Uniform uvector = apply(cbind(obsx. coef(fit)["shape"]) colnames(dmatrix) = c("mu". rollframe = ) head(tail(dji3 ret[. data = dji3 ret[.model = "nig") fit = ugarchfit(spec. 23(3). 55(2). mu = x[2]. the test of the tail at the “alpha” quantile level is performed using a censored normal likelihood. M. and Bera. Usage DACTest(forecast.1). actual. significance = .test=TRUE) ## End(Not run) DACTest Directional Accuracy Test Description Implements the Directional Accuracy Test of Pesaran and Timmerman and Excess Profitability Test of Anatolyev and Gerko. The confidence level at which the Null Hypothesis is evaluated.test=TRUE) test3 = BerkowitzLR(data = nvector. lags = 1.DACTest 35 # hist(uvector) # transform to N( . Choice of Pesaran and Timmermann (‘PT’) or Anatolyev and Gerko (‘AG’) tests. conf. The test statistic.level = . and distributed as N(0.level. 5. 5. A numeric vector of the actual (realized) values. . test = c("PT". 1.level Details See the references for details on the tests. 5. "AG"). alpha = . tail. The Null Hypothesis. alpha = . tail. significance = . A numeric vector of the forecasted values.95) Arguments forecast actual test conf. Whether to reject or not the Null given the conf. Value A list with the following items: Test Stat p-value H Decision DirAcc The type of test performed. significance = . 5) test2 = BerkowitzLR(data = nvector. The directional accuracy of the forecast.1) nvector = qnorm(uvector) test1 = BerkowitzLR(data = nvector. The p-value of the test statistic. The Null is effectively that of independence. out.1]. A trading approach to testing for predictability. This is not reflected in this data set as that would bring the starting date of the data to 2001. and Timmermann. Journal of Business and Economic Statistics. 23(4).95)) print(DACTest(forc.mean = TRUE). 1992.model = list(model = "gjrGARCH"). test = "AG". Usage data(dji3 ret) Format A data. n.rollframe="all". Examples ## Not run: data(dji3 ret) spec = ugarchspec(mean. S.which="series")) print(DACTest(forc. 10(4).ahead = 1.model = list(armaOrder = c(6.align=FALSE.data. conf. conf. 2008. A.level = . and Gerko.numeric(as. Pesaran.95)) ## End(Not run) dji3 ret data: Dow Jones 30 Constituents Closing Value Log Return Description Dow Jones 30 Constituents closing value log returns from 1987-03-16 to 2009-02-03 from Yahoo Finance. Source Yahoo Finance . 455–461. include.level = . distribution. variance. obsx. drop = FALSE].H. n.model = "nig") fit = ugarchfit(spec. obsx. Note that AIG was replaced by KFT (Kraft Foods) on September 22. 1 ) forc = as. Journal of Business and Economic Statistics.frame(pred. data = dji3 ret[. 2005.roll = 999) # Get Realized (Oberved) Data obsx = tail(dji3 ret[.frame containing 30x5521 observations.36 Author(s) Alexios Ghalanos References dji30ret Anatolyev. 461–465.1). A simple nonparametric test of predictive performance. A. test = "PT". M. 1.sample = 1 ) pred = ugarchforecast(fit. 2.org/jbes/View/ References Bollerslev.S. 14. E. Usage data(dmbp) Format A data. The daily percentage nominal returns computed as 100 [ln(Pt) . ForwardDates-methods function: Generate Future Dates Description Given a starting date. The variables in the data set are: 1.S.format. Usage ForwardDates(Dates.ln(Pt-1)]. and Ghysels. periodicity = "days") . 1996. Periodic Autoregressive Conditional Heteroscedasticity . dollar rates. where Pt is the bilateral Deutschemark/British pound rate constructed from the corresponding U. this helper function generates a set of future dates (excl. T.dmbp 37 dmbp data: Deutschemark/British pound Exchange Rate Description The Bollerslev-Ghysel benchmark dataset. dollar market during regular European trading hours and 0 otherwise.amstat. date.weekends) for use in forecasting and simulation when using external regressors.ahead. A dummy variable that takes the value of 1 on Mondays and other days following no trading in the Deutschemark or British pound/ U. 139–151. n. Journal of Business and Economic Statistics. Source JBES Data Archive ftp://www.frame containing 2x1974 observations. n. weekday = "Monday") ## End(Not run) GARCHboot-class class: GARCH Bootstrap Class Description High Level GARCH bootstrap class to hold the univariate and multivariate boot objects.38 Arguments Dates n. The format of the dates e. The last date is used as the starting date for the forward date creation. date. For example. date. one needs a set of forward deterministic dummy variables for the Mondays going forward.ahead date. Note GARCHboot-class A character vector of dates.g.ahead=1 . The number of dates to generate forward.character(fwd1 ).format = "%Y-%m-%d". “%Y-%m-%d"” . if fitting a GARCH model with a "Monday" dummy variable in the mean equation. then for simulation or forecasting. Author(s) Alexios Ghalanos Examples ## Not run: data(sp5 ret) Dates = rownames(sp5 ret) # generate the 1 forward non-weekend days fwd1 = ForwardDates(Dates. Objects from the Class A virtual Class: No objects may be created from it. periodicity = "days") # create a dummy vector for those forward days which are Mondays fwdMonday = WeekDayDummy(as. This is a helper function particularly useful when used with the weekday dummy variable for simulation and forecasting in light of weekday dummy external regressors in the mean or variance equation.format = "%Y-%m-%d". Currently only days is supported. .format periodicity Value A POSIXct vector of future dates. Author(s) Alexios Ghalanos Examples showClass("GARCHboot") 39 GARCHdistribution-class class: GARCH Parameter Distribution Class Description High Level GARCH parameter distribution class to hold the univariate and multivariate boot objects. Methods No methods defined with class "GARCHdistribution" in the signature.GARCHdistribution-class Extends Class "rGARCH". Extends Class "rGARCH". Author(s) Alexios Ghalanos Examples showClass("GARCHdistribution") . Objects from the Class A virtual Class: No objects may be created from it. directly. Methods No methods defined with class "GARCHboot" in the signature. directly. Methods No methods defined with class "GARCHfit" in the signature. Author(s) Alexios Ghalanos Examples showClass("GARCHfilter") GARCHfit-class class: GARCH Fit Class Description High Level GARCH fit class to hold the univariate and multivariate fits objects. Methods No methods defined with class "GARCHfilter" in the signature. Objects from the Class A virtual Class: No objects may be created from it. directly. . Extends Class "rGARCH". Objects from the Class A virtual Class: No objects may be created from it. directly.40 GARCHfit-class GARCHfilter-class class: GARCH Filter Class Description High Level GARCH filter class to hold the univariate and multivariate filter objects. Extends Class "rGARCH". Extends Class "rGARCH". Methods No methods defined with class "GARCHforecast" in the signature.GARCHforecast-class Author(s) Alexios Ghalanos 41 Examples showClass("GARCHfit") GARCHforecast-class class: GARCH Forecast Class Description High Level GARCH forecast class to hold the univariate and multivariate forecast objects. Author(s) Alexios Ghalanos Examples showClass("GARCHforecast") . Objects from the Class A virtual Class: No objects may be created from it. directly. Methods No methods defined with class "GARCHroll" in the signature. Methods No methods defined with class "GARCHpath" in the signature. directly. directly. .42 GARCHroll-class GARCHpath-class class: GARCH Path Simulation Class Description High Level GARCH Path simulation class to hold the univariate and multivariate path simulation objects. Extends Class "rGARCH". Author(s) Alexios Ghalanos Examples showClass("GARCHpath") GARCHroll-class class: GARCH Roll Class Description High Level GARCH roll class to hold the univariate and multivariate roll objects. Objects from the Class A virtual Class: No objects may be created from it. Extends Class "rGARCH". Objects from the Class A virtual Class: No objects may be created from it. Author(s) Alexios Ghalanos Examples showClass("GARCHsim") . Objects from the Class A virtual Class: No objects may be created from it. Methods No methods defined with class "GARCHsim" in the signature. directly. Extends Class "rGARCH".GARCHsim-class Author(s) Alexios Ghalanos 43 Examples showClass("GARCHroll") GARCHsim-class class: GARCH Simulation Class Description High Level GARCH simulation class to hold the univariate and multivariate simulation objects. Methods No methods defined with class "GARCHspec" in the signature. . Methods No methods defined with class "GARCHtests" in the signature. directly. directly. Extends Class "rGARCH". Objects from the Class A virtual Class: No objects may be created from it. Extends Class "rGARCH". Objects from the Class A virtual Class: No objects may be created from it. Author(s) Alexios Ghalanos Examples showClass("GARCHspec") GARCHtests-class class: GARCH Tests Class Description GARCH High level inference and other tests class.44 GARCHtests-class GARCHspec-class class: GARCH Spec Class Description High Level GARCH spec class to hold the univariate and multivariate spec objects. ghyptransform Author(s) Alexios Ghalanos Examples showClass("GARCHtests") 45 ghyptransform Distribution: Generalized Hyperbolic Transformation and Scaling Description The function scales the distributions from the (0, 1) zeta-rho GARCH parametrization to the alphabeta parametrization and performs the appropriate scaling to the parameters given the estimated sigma and mu. Usage ghyptransform(mu = Arguments mu sigma Either the conditional time-varying (vector) or unconditional mean estimated from the GARCH process. , sigma = 1, skew = , shape = 3, lambda = - .5) The conditional time-varying (vector) sigma estimated from the GARCH process. skew, shape, lambda The conditional non-time varying skewness (rho) and shape (zeta) parameters estimated from the GARCH process (zeta-rho), and the GHYP lambda parameter (‘dlambda’ in the estimation). Details The GHYP transformation is taken from Rmetrics internal function and scaled as in Blaesild (see references). Value A matrix of size nrows(sigma) x 4 of the scaled and transformed parameters to be used in the alpha-beta parametrized GHYP distribution functions. Author(s) Diethelm Wuertz for the Rmetrics R-port of the nig transformation function. Alexios Ghalanos for rugarch implementation. 46 References multifilter-methods Blaesild, P. 1981, The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen’s bean data, Biometrika, 68, 251–263. Eberlein, E. and Prauss, K. 2000, The Generalized Hyperbolic Model Financial Derivatives and Risk Measures, Mathematical Finance Bachelier Congress, 245–267. multifilter-methods function: Univariate GARCH and ARFIMA Multiple Filtering Description Method for multiple filtering of a variety of univariate GARCH and ARFIMA models. Usage multifilter(multifitORspec, data = NULL, out.sample = , n.old = NULL, parallel = FALSE, parallel.control = list(pkg = c("multicore", "snowfall"), cores = 2), ...) Arguments multifitORspec Either a univariate GARCH or ARFIMA multiple fit object of class uGARCHmultifit and ARFIMAmultifit, or alternatively a univariate GARCH or ARFIMA multiple specification object of class uGARCHmultispec and ARFIMAmultispec with valid parameters supplied via the fixed.pars argument in the individual specifications. data Required if a multiple specification rather than a multiple fit object is supplied. A multivariate data object. Can be a matrix or data.frame object, no other class supported at present. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (as in ugarchfit function). For comparison with uGARCHfit or ARFIMAfit models using the out.sample argument, this is the length of the original dataset (see details). out.sample n.old parallel Whether to make use of parallel processing on multicore systems. parallel.control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S), and the number of cores to make use of. ... Value A uGARCHmultifilter object containing details of the multiple GARCH filter. A ARFIMAmultifilter object containing details of the multiple ARFIMA filter. . multifit-methods Author(s) Alexios Ghalanos 47 multifit-methods function: Univariate GARCH and ARFIMA Multiple Fitting Description Method for multiple fitting a variety of univariate GARCH and ARFIMA models. Usage multifit(multispec, data, out.sample = , solver = "solnp", solver.control = list(), fit.control = list(stationarity = 1, fixed.se = , scale = ), parallel = FALSE, parallel.control = list(pkg = c("multicore", "snowfall"), cores = 2), ...) Arguments multispec out.sample data solver fit.control A multiple GARCH or ARFIMA spec object of class uGARCHmultispec and ARFIMAmultispec. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (see details). A multivariate data object. Can be a matrix or data.frame object, no other class supported at present. One of either “nlminb” or “solnp”. Control arguments passed to the fitting routine. Stationarity (only for the GARCH case) explicitly imposes the variance stationarity constraint during optimization. The fixed.se argument controls whether standard errors should be calculated for those parameters which were fixed (through the fixed.pars argument of the ugarchspec or arfimaspec functions). The scale parameter controls whether the data should be scaled before being submitted to the optimizer. solver.control Control arguments list passed to optimizer. parallel Whether to make use of parallel processing on multicore systems. parallel.control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S), and the number of cores to make use of. ... Value A uGARCHmultifit or ARFIMAmultifit object containing details of the GARCH or ARFIMA fits. . sample = . else it must be of same length as the data column dimension. data = NULL. If a specification object is supplied.. n = 4) ) fitlist = multifit(multispec = mspec. n. no other class supported at present.roll = . indicates how many data points to keep for out of sample testing.roll out.ahead = 1.control = list(pkg = c("multicore".function in the individual specifications. out. .) Arguments multifitORspec Either a univariate GARCH or ARFIMA multiple fit object uGARCHmultifit and ARFIMAmultifit. parallel. Can be a matrix or data.ahead n. . vregfor = NULL). "snowfall"). data Required if a multiple specification rather than a multiple fit object is supplied. The no. A multivariate data object.1:4]) ## End(Not run) multiforecast-methods multiforecast-methods function: Univariate GARCH and ARFIMA Multiple Forecasting Description Method for multiple forecasting from a variety of univariate GARCH and ARFIMA models. parallel = FALSE. then it will be replicated to that dimension.frame object. Usage multiforecast(multifitORspec. n. data = dji3 ret[. If this is not a vector equal to the column dimension of the data.forecasts A list with forecasts for the external regressors in the mean and/or variance equations if specified. or alternatively a univariate GARCH or ARFIMA multiple specification object of class uGARCHmultispec and ARFIMAmultispec with valid parameters supplied via the setfixed<.48 Author(s) Alexios Ghalanos Examples ## Not run: data(dji3 ret) spec = ugarchspec() mspec = multispec( replicate(spec. The forecast horizon.sample Optional. external.. external.forecasts = list(mregfor = NULL. n. cores = 2). of rolling forecasts to create beyond the first one. Value A uGARCHmultiforecast or ARFIMAmultiforecast object containing details of the multiple GARCH or ARFIMA forecasts.. See the class for details.multispec-methods parallel Whether to make use of parallel processing on multicore systems. Author(s) Alexios Ghalanos .control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S). Value A uGARCHmultispec or ARFIMAmultispec object containing details of the multiple GARCH or ARFIMA specifications. multispec-methods function: Univariate multiple GARCH Specification Description Method for creating a univariate multiple GARCH or ARFIMA specification object prior to fitting. filtering and forecasting). . 49 parallel. and the number of cores to make use of. Usage multispec( speclist ) Arguments speclist A list with as many univariate GARCH or ARFIMA specifications of class uGARCHspec and ARFIMAspec as there will be columns in the data object passed to one of the other methods which uses a multiple specification object (fitting.. Author(s) Alexios Ghalanos . random generation and fitting from the univariate distributions implemented in the rugarch package. . with functions for skewness and excess kurtosis given density skew and shape parameters.50 Examples # how to make a list with 2 uGARCHspec objects of the same type spec = ugarchspec() mspec = multispec( replicate(2. quantile function. MLE parameter fit for the rugarch univariate distributions.. rgarchdist fitdist rugarch univariate distributions. 2) does not work. Objects from the Class A virtual Class: No objects may be created from it. n = 2) # or simply combine disparate objects spec1 = ugarchspec(distribution = "norm") spec2 = ugarchspec(distribution = "std") mspec = multispec( c( spec1. distribution function. spec) ) # note that replicate(spec.e. spec2 ) ) rgarchdist rGARCH-class class: rGARCH Class Description Highest Level Virtual Package Class to which all other classes belong. Methods No methods defined with class "rGARCH" in the signature. Author(s) Alexios Ghalanos Examples showClass("rGARCH") rgarchdist Distribution: rugarch distribution functions Description Density.be careful about the order # else explicity name ’n’ (i.. lambda = . the shape. lambda = . mu.5. mu = . p.. The “dskewness” and “dkurtosis” functions take as inputs the distribution name. 51 5. The functions are not at present vectorized. A numeric vector of probabilities. lambda = . x. shape = 5) fitdist(distribution = "norm". skew and lambda are transformed from the ‘zeta-rho’ to the ‘alpha-beta’ parametrization and then scaled by the mean and standard deviation. skew and shape parameters and return the skewneness and excess kurtosis of the distribution. distribution lambda n p y.. Value d* returns the density. p* returns the distribution function. q. sigma = 1. scale and skewness and shape parameters (see details). Control parameters passed to the solnp solver. “std”. “nig”. “sstd”. all values are numeric vectors. n.5.rgarchdist Usage ddist(distribution = "norm". sigma = 1. lambda = . The additional shape parameter for the Generalized Hyperbolic and NIG distributions. The fitting routines use the solnp solver and minimize the negative of the log-likelihood. mu = . control=list()) dskewness(distribution = "norm". skew = 1. shape location. q* returns the quantile function. and r* generates random deviates. skew. . A numeric vector of quantiles.5) 5. shape = Arguments lambda = . skew = 1. sigma.. q x control Details For the dQuotenig and “ghyp” distributions. shape = 5) rdist(distribution = "norm". sigma = 1. A univariate dataset (for fitting routine). The likelihood values of the optimization (vector whose length represents the number of major iterations). skew = 1. “sged”. skew = 1.. “jsu”.. shape = dkurtosis(distribution = "norm". mu = .5. sigma = 1. mu = . Valid choices are “norm”. The number of observations. fitdist returns a list with the following components: par value The best set of parameters found. shape = 5) qdist(distribution = "norm".5) The distribution name. y. skew = 1.5. “ged”. lambda = . shape = 5) pdist(distribution = "norm". skew = 1. “snorm”.. dskewness returns the skewness of the distribution. On Bayesian Modelling of Fat Tails and Skewness. A. “sstd”. “ged”. mimeo: Univ.J. 283–291. and Stasinopoulos D. 1998. N. L. M for the JSU distribution in the gamlss package. and Steel. sp5 ret data: Standard and Poors 500 Closing Value Log Return Description The S\&P500 index closing value log return from 1987-03-10 to 2009-01-30 from yahoo finance. The hessian at the solution. Rigby. Usage data(sp5 Format A data.of Aarhus Denmark. 5. Author(s) Diethelm Wuertz for the Rmetrics R-port of the “norm”. Source Yahoo Finance ret) . Fernandez C. 359–371. Barndorff-Nielsen. O.52 convergence lagrange h xineq An integer code. Journal of the American Statistical Association. “sged” and “nig” distrbutions.F. M.frame containing 1x5523 observations. 1954. sp500ret The value of the inequality constraint multiplier (NULL for the distribution fit problems). Systems of frequency curves derived from the first law of Laplace. dkurtosis returns the excess kurtosis of the distribution. 1995. The lagrange multiplier value at convergence. “snorm”. References Johnson. R. Normal inverse Gaussian processes and the modeling of stock returns. Alexios Ghalanos for rugarch implementation and higher moment distribution functions. Trabajos de Estadistica. “std”. E. 0 indicates successful convergence. "published") ) Arguments benchmark Details Currently. 2 benchmark suites are available. 1271–1276. 107(443). The “commercial” option runs the standard GARCH.htm References Brooks. Usage ugarchbench( benchmark = c("commercial".stanford. C. apARCH and gjrGARCH against a commercial based product and reports the results. Examples ugarchbench( benchmark = "published") The type of benchmark to run against (see details). Author(s) Alexios Ghalanos Source http://www.ugarchbench 53 ugarchbench Benchmark: The Benchmark Test Suite Description Function for running the rugarch benchmark suite. . The “published” option is based on the published benchmark of Bollerslev and Ghysels for the standard and exponential GARCH models on the dmbp data. 1997. Economic Journal.edu/~clint/bench/index. The data for this bechmarks is “AA” in the dji30ret dataset. GARCH Modelling in Finance: A review of the Software Options. The plot option which relates to either a numeric choice (1:3). Objects from the Class A virtual Class: No objects may be created from it. c(0. an interactive choice (“ask” which is the default) and an all plot choice (“all”) for which only plots 2 and 3 are included.95) ). 2004.data. E. 2006. 0. “summary” for summary statistics per n. for which the option qtile is then required and takes a numeric vector of quantiles (e.54 uGARCHboot-class uGARCHboot-class class: Univariate GARCH Bootstrap Class Description Class for the univariate GARCH Bootstrap based Forecasts. Romo. L. Extends Class "GARCHboot". Computational Statistics and Data Analysis.data. Pascual. E.ahead distribution.. with the options “raw” for the bootstrapped series.ahead bootstrapped series. L. The plot method provides for a Parameter Density Plots (only valid for the “full” method). show signature(object = "uGARCHboot"): bootstrap forecast summary. See Also Classes uGARCHforecast. Bootstrap prediction for returns and volatilities in GARCH models. and Ruiz. Note The as.frame function takes optionally the arguments which. Journal of Time Series Analysis. and Ruiz. directly.05. plot signature(x = "uGARCHboot". the argument type. Methods as. Class "rGARCH". y = "missing"): bootstrap forecast plots. and the series and sigma forecast plots with quantile error lines from the bootstrapped n.g.ahead. Bootstrap predictive inference for ARIMA processes. by class "GARCHboot". Romo. uGARCHfit and uGARCHspec. being either “sigma” or “series”.frame signature(x = "uGARCHboot"): extracts various values from object (see note). Author(s) Alexios Ghalanos References Pascual. J. .. distance 2. J. and “q” for the quantiles of the n. If a specification object is supplied. data method n. Optional. indicates how many data points to keep for out of sample testing. Either the full or partial bootstrap (see note).bootfit + n.forecasts A list with forecasts for the external regressors in the mean and/or variance equations if specified.ahead forecasts used to generate the predictive density. simply the number of random samples from the empirical distribution to generate per n.function in the specification.forecasts = list(mregfor = NULL.bootfit = 1 . Required if a specification rather than a fit object is supplied. One of either “nlminb” or “solnp”. solver. method = c("Partial". .bootpred).bootpred = 5 . cores = 2)) Arguments fitORspec Either a univariate GARCH fit object of class uGARCHfit or alternatively a univariate GARCH specification object of class uGARCHspec with valid parameters supplied via the setfixed<. rseed = NA. If this is for the partial method. Usage ugarchboot(fitORspec. external.sample rseed solver solver. n. The forecast horizon. Not relevant for the “Partial” method. The number of bootstrap replications per parameter distribution per n.e the parameter uncertainty). data = NULL. fit.bootpred out. n.control = list(pkg = c("multicore". external.bootfit n. parallel = FALSE.ahead n. out.ugarchboot-methods 55 ugarchboot-methods function: Univariate GARCH Forecast via Bootstrap Description Method for forecasting the GARCH density based on a bootstrap procedures (see details and references). A vector of seeds to initialize the random number generator for the resampling with replacement method (if supplied should be equal to n. "Full"). fit. n.control = list().control Control arguments list passed to optimizer.control Control arguments passed to the fitting routine (as in the ugarchfit method). The number of simulation based re-fits used to generate the parameter distribution (i. vregfor = NULL). "snowfall").control = list().ahead = 1 . parallel. solver = "solnp". parallel Whether to make use of parallel processing on multicore systems.ahead.sample = . is very time consuming which is why the parallel option (as in the ugarchdistribution is available and recommended). takes into account parameter uncertainty by building a simulated distribution of the parameters through simulation and refitting..1).mean=TRUE. garchOrder=c(1. .. Pascual. E. arfima=FALSE. See Also For specification ugarchspec. 2006.. E. namely that arising from the form of the predictive density and due to parameter estimation. drop = FALSE].. J. L. Details There are two main sources of uncertainty about n. Author(s) Alexios Ghalanos References Pascual. Value A uGARCHboot object containing details of the GARCH bootstrapped forecast density.model=list(model="gjrGARCH". Computational Statistics and Data Analysis.1)). mean. will not generate prediction intervals for the sigma 1-ahead forecast for which only the parameter uncertainty is relevant in GARCH type models. .control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S). Romo.ahead forecasting from GARCH models. Bootstrap predictive inference for ARIMA processes. J. out. based on the referenced paper by Pascual et al. .sample = . The “full” method. include. only considers distribution uncertainty and while faster. rolling forecast and estimation ugarchroll.56 ugarchboot-methods parallel. forecasting ugarchforecast. This process. distribution. and the number of cores to make use of. parameter distribution and uncertainty ugarchdistribution. and Ruiz. Bootstrap prediction for returns and volatilities in GARCH models. and Ruiz. L. while more accurate. fitting ugarchfit. Romo. The “partial” method. Journal of Time Series Analysis. is based on resampling innovations from the empirical distribution of the fitted GARCH model to generate future realizations of the series and sigma. filtering ugarchfilter. Examples ## Not run: data(dji3 ret) spec = ugarchspec(variance. "BA". archpow = 1).model="std") ctrl = list(tol = 1e-7. simulation ugarchsim. delta = 1e-9) fit = ugarchfit(data=dji3 ret[. The bootstrap method considered here. archm = FALSE. 2004.model=list(armaOrder=c(1. solver. by class "GARCHdistribution". The standard option for which is used. . allowing for a numeric arguments to one of the four plot types else interactive choice via “ask”. namely window which indicates the particular distribution window number for which data is required (is usually just 1 unless the recursive option was used).data. unconditional variance and mean.frame function takes optionally 2 additional arguments. Bivariate Plots (take window as additional argument). qtile = c( . fit.bootpred = 2 bootpred # as.frame(bootpred. The plot method offers 4 plot types. solver = "solnp".data. “stats” for various statistics computed for the simulations such as log likelihood. n.control = list(scale = 1)) bootpred = ugarchboot(fit. Stats and RMSE (only when recursive option used) Plots. the parameter distribution and is the default choice). the parameter standard error distribution). n. Valid values for the latter are “rmse” for the root mean squared error between simulation fit and actual parameters.uGARCHdistribution-class spec = spec. Class "rGARCH".e. which = "sigma". 1.e. and which indicating the type of data required. plot signature(x = "uGARCHdistribution".ahead = 12 . Parameter Density Plots (take window as additional argument). 5)) ## End(Not run) 57 ) uGARCHdistribution-class class: Univariate GARCH Parameter Distribution Class Description Class for the univariate GARCH Parameter Distribution. Extends Class "GARCHdistribution". and “coefse” for the estimated robust standard errors of the coefficients (i. . Methods as. method = "Partial". distance 2. Note The as.data. show signature(object = "uGARCHdistribution"): Parameter Distribution Summary.frame signature(x = "uGARCHdistribution"): Extracts various values from object (see note). namely. Objects from the Class A virtual Class: No objects may be created from it. “coef” for the estimated coefficients (i. type = "q". persistence. directly. y = "missing"): Parameter Distribution Plots.control = ctrl. n. recursive. recursive = FALSE. uGARCHfit and uGARCHspec..sample = spec = spec. recursive. presigma = NA. rseed = NA.1).sim = 2 ## End(Not run) . . parallel.start . garchOrder=c(1. vexsimdata = NULL. arfima=FALSE.control = list(). "snowfall"). solver. mexsimdata = NULL. out. The burn-in sample.length = 6 .control = list(pkg = c("multicore". mean. distfit = NA). m. solver = "solnp") dist = ugarchdistribution(fit. archpow = 1).control = list(). The simulation horizon.) Arguments fitORspec Either a univariate GARCH fit object of class uGARCHfit or alternatively a univariate GARCH specification object of class uGARCHspec with valid parameters supplied via the setfixed<. cores = 2). prereturns = NA. m. . parallel = FALSE.sim n. archm = FALSE. custom. n.function in the specification. n. n..sim = 5) ugarchdistribution-methods function: Univariate GARCH Parameter Distribution via Simulation Description Method for simulating and estimating the parameter distribution from a variety of univariate GARCH models as well as the simulation based consistency of the estimators given the data size.dist = list(name = NA. preresiduals = NA. fit. drop = FALSE].sim = 1 .start = 5 . Usage ugarchdistribution(fitORspec. include.sim = 2 .model="std") fit = ugarchfit(data=sp5 ret[.58 Author(s) Alexios Ghalanos See Also Classes uGARCHforecast.mean=TRUE.model=list(model="gjrGARCH". n.window = 1 .start = 1.1)). 1. solver = "solnp".model=list(armaOrder=c(1. Examples ugarchdistribution-methods ## Not run: data(sp5 ret) spec = ugarchspec(variance. distribution. ugarchdistribution-methods m. in the sense of the root mean square error (rmse) of the difference between the simulated and true (hypothesized) parameters. it determines the total number of separate and increasing length windows which will be simulated and fitted.length If recursive is TRUE. this indicates the final length of the simulation horizon. The recursive option also allows the evaluation of the simulation based consistency (in terms of sqrt(N) ) of the parameters as the length (n. Details This method facilitates the simulation and evaluation of the uncertainty of GARCH model parameters. One of either “nlminb” or “solnp”. parallel.sim) of the data increases. If the fit object contains external regressors in the mean equation. This is a very expensive function. solver.control Allows the starting sigma values to be provided by the user.. recursive. 59 recursive Whether to perform a recursive simulation on an expanding window. this indicates the increment to the expanding window. .. Optional density with fitted object from which to simulate. performing many re-fits of the simulated data in order to generate the parameter distribution and it is therefore suggested that. . this must be provided. Allows the starting residuals to be provided by the user. particularly if using the recursive option. with starting length n. the parallel functionality should be used (in a system with ideally many cores and at least 4GB of RAM for the recursion option. Control arguments passed to the fitting routine (as in the ugarchfit method).window If recursive is TRUE.. .control Control arguments list passed to optimizer.. Matrix of simulated external regressor-in-mean data.sim The number of simulations.dist mexsimdata vexsimdata solver fit.length. if available.control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S). Value A uGARCHdistribution object containing details of the GARCH simulated parameters distribution. parallel Whether to make use of parallel processing on multicore systems. presigma prereturns preresiduals rseed custom.).sim. and the number of cores to make use of. both on memory and cpu resources. Allows the starting return data to be provided by the user. recursive. Together with recursive. Matrix of simulated external regressor-in-variance data. Optional seeding value(s) for the random number generator. this must be provided. If the fit object contains external regressors in the variance equation. frame signature(x = "uGARCHfilter"): extracts the position (dates). . gof signature(object = "uGARCHfilter". fitting ugarchfit. groups = "numeric"): calculates and returns the adjusted goodness of fit statistic and p-values for the fitted distribution based on the Vlaar and Palm paper (1993). coef signature(object = "uGARCHfilter"): extracts the coefficients. distribution = "missing". Groups is a numeric vector of bin sizes. data. Extends Class "GARCHfilter". pars = "missing". signbias signature(object = "uGARCHfilter"): calculates and returns the sign bias test of Engle and Ng (1993). by class "GARCHfilter". newsimpact signature(object = "uGARCHfilter"): calculates and returns the news impact curve. uGARCHfilter-class class: Univariate GARCH Filter Class Description Class for the univariate GARCH filter. residuals signature(object = "uGARCHfilter"): extracts the residuals.60 Author(s) Alexios Ghalanos See Also uGARCHfilter-class For specification ugarchspec. distribution = "missing". model = "missing"): calculates and returns the halflife of the garch fit variance given a uGARCHfilter object. persistence signature(object = "uGARCHfilter". simulation ugarchsim. distance 2. Methods as. fitted signature(object = "uGARCHfilter"): extracts the fitted values. directly. residuals and conditional sigma. fitted values. infocriteria signature(object = "uGARCHfilter"): calculates and returns various information criteria. forecasting ugarchforecast. Class "rGARCH". likelihood signature(object = "uGARCHfilter"): extracts the likelihood. bootstrap forecast ugarchboot.data. filtering ugarchfilter. pars = "missing". submodel = "missing"): calculates and returns the persistence of the garch filter model. model = "missing". halflife signature(object = "uGARCHfilter". rolling forecast and estimation ugarchroll. sigma signature(object = "uGARCHfilter"): extracts the conditional sigma values. solver = "solnp".pars = as.e the optimization process) such as the nyblom test. spec = spec. inner.1). mean. plot signature(x = "uGARCHfilter".fit)) c(uncvariance(sgarch.fit)) c(uncmean(sgarch. y = "missing"): filter plots show signature(object = "uGARCHfilter"): filter summary. ARMAX.fit)) ## End(Not run) ugarchfilter-methods function: Univariate GARCH Filtering Description Method for filtering a variety of univariate GARCH models. arch-in-mean). Author(s) Alexios Ghalanos Examples ## Not run: data(dji3 ret) ctrl = list(rho = 1. uncvariance signature(object = "uGARCHfilter". solver. include. distribution. garchOrder = c(1. distribution = "missing". likelihood(sgarch. uncmean(sgarch.filter). mean.1)). distribution.filter = ugarchfilter(data = dji3 ret[.1).model = list(model = "sGARCH".fit = ugarchfit(data = dji3 ret[. Note The uGARCHfilter class contains almost all the methods available with the uGARCHfit with the exception of those requiring the scores of the likelihood (i.1)). . garchOrder = c(1.drop=FALSE].list(coef(sgarch.model = list(armaOrder = c(1. model = "missing".model = "std". pars = "missing". submodel = "missing"): calculates and returns the long run unconditional variance of the garch filter given a uGARCHfilter object. uncvariance(sgarch.fit))) sgarch. include.control = ctrl) spec = ugarchspec(variance.mean = TRUE).drop=FALSE]."AA".iter = 1 ."AA". spec = spec) c(likelihood(sgarch.filter).model = list(model = "sGARCH". fixed.model = list(armaOrder = c(1. delta = 1e-8.model = "std") sgarch.filter).mean = TRUE). tol = 1e-6) spec = ugarchspec(variance.iter = 65 .ugarchfilter-methods 61 uncmean signature(object = "uGARCHfilter"): calculates and returns the unconditional mean of the conditional mean equation (constant. outer. The reason for using this is so that the old and new datasets agree since the original recursion uses the sum of the residuals to start the recursion and therefore is influenced by new data. Author(s) Alexios Ghalanos See Also For specification ugarchspec. Can be a numeric vector. data. include.old argument is optional and indicates the length of the original data (in cases when this represents a series augmented by newer data). xts.MINIT = 65 .frame.model = list(model = "eGARCH". forecasting ugarchforecast. Details ugarchfilter-methods A univariate data object.DELTA = 1e-8. zoo.sample n. A univariate GARCH spec object of class uGARCHspec with the fixed. garchOrder = c(1. Value A uGARCHfilter object containing details of the GARCH filter.1)). ts or irts object.old=NULL.sample argument.old . For a small augmentation the values converge after x periods. but it is sometimes preferable to have this option so that there is no forward looking information contaminating the study. The n.model = list(armaOrder = c(1.pars argument having the model parameters on which the filtering is to take place.control = ctrl) .1). rolling forecast and estimation ugarchroll. solver = "solnp". fitting ugarchfit.drop=FALSE].. distribution. solver. bootstrap forecast ugarchboot. simulation ugarchsim. mean..) Arguments data spec out. data. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (as in ugarchfit function). For comparison with uGARCHfit models using the out. matrix. this is the length of the original dataset (see details).fit = ugarchfit(data = sp5 ret[. spec = spec. timeSeries.62 Usage ugarchfilter(spec. parameter distribution and uncertainty ugarchdistribution. Examples ## Not run: data(sp5 ret) ctrl = list(RHO = 1. .TOL = 1e-6) spec = ugarchspec(variance.1.mean = TRUE)..MAJIT = 1 .sample = .model = "std") egarch. out.. n. . distribution.fit))) egarch. directly. infocriteria signature(object = "uGARCHfit"): Calculates and returns various information criteria.1).model = list(armaOrder = c(1. Objects from the Class A virtual Class: No objects may be created from it.1)). fitted values. Extends Class GARCHfit. Groups is a numeric vector of bin sizes.uGARCHfit-class spec = ugarchspec(variance. model: Object of class "vector" The model specification common to all objects.drop=FALSE]. signbias signature(object = "uGARCHfit"): Calculates and returns the sign bias test of Engle and Ng (1993). data.data. Methods as. nyblom signature(object = "uGARCHfit"): Calculates and returns the Hansen-Nyblom stability test (1990). Class rGARCH.model = "std".frame signature(x = "uGARCHfit"): Extracts the position (dates).mean = TRUE). coef signature(object = "uGARCHfit"): Extracts the coefficients.pars = as. fixed.model = list(model = "eGARCH".filter = ugarchfilter(data = sp5 ret[. . gof signature(object = "uGARCHfit". Additional logical option of ‘robust’ indicates whether to extract the robust based covariance matrix. distance 2. Slots fit: Object of class "vector" Holds data on the fitted model.list(coef(egarch. groups = "numeric"): Calculates and returns the adjusted goodness of fit statistic and p-values for the fitted distribution based on the Vlaar and Palm paper (1993). residuals and conditional sigma. spec = spec) ## End(Not run) 63 uGARCHfit-class class: Univariate GARCH Fit Class Description Class for the univariate GARCH fit.1. by class GARCHfit. garchOrder = c(1. mean. vcov signature(object = "uGARCHfit"): Extracts the covariance matrix of the parameters. include. newsimpact signature(object = "uGARCHfit"): Calculates and returns the news impact curve. Note Methods for coef. plot signature(x = "uGARCHfit". getspec signature(object = "uGARCHfit"): Extracts and returns the GARCH specification from a fit object. persistence signature(object = "uGARCHfit". submodel = "ANY". halflife signature(object = "missing". Method for plot provides for interactive choice of plots. pars = "numeric". distribution = "character". residuals signature(object = "uGARCHfit"): Extracts the residuals. distribution = "character". uncvariance signature(object = "uGARCHfit". model = "missing". pars = "numeric". The data. model = "character"): Calculates and returns the persistence of the GARCH fit model given a named parameter vector as returned by the fit. fitted signature(object = "uGARCHfit"): Extracts the fitted values. the original data. likelihood. ARMAX. a distribution model name and a GARCH model name with a submodel included if the model is of the nested type such as fGARCH. pars = "numeric". distribution="missing". distribution = "character". Method for show gives detailed summary of GARCH fit with various tests. model = "missing"): Calculates and returns the persistence of the GARCH fit model given a uGARCHfit object. uGARCHfit-class sigma signature(object = "uGARCHfit"): Extracts the conditional sigma values. y = "missing"): Fit plots. a distribution model name and a GARCH model name with a submodel included if the model is of the nested type such as fGARCH and any external regressor data. vexdata = "ANY"): Calculates and returns the long run unconditional variance of the GARCH fit given a named parameter vector as returned by the fit. distribution = "missing".64 likelihood signature(object = "uGARCHfit"): Extracts the likelihood. pars = "missing". halflife signature(object = "uGARCHfit". a distribution model name and a GARCH model name with a submodel included if the model is of the nested type such as fGARCH.frame method returns a data frame with 4 columns. vexdata = "missing"): Calculates and returns the long run unconditional variance of the GARCH fit given a uGARCHfit object. persistence signature(object = "missing". show signature(object = "uGARCHfit"): Fit summary. distribution = "missing". pars = "missing". the . convergence signature(object = "uGARCHfit"): Returns the solver convergence code for the fitted object (zero denotes convergence). arch-in-mean). option of choosing a particular plot (option “which” equal to a valid plot number) or a grand plot including all subplots on one page (option “which”=“all”). uncmean signature(object = "uGARCHfit"): Calculates and returns the unconditional mean of the conditional mean equation (constant. model = "character"): Calculates and returns the halflife of the GARCH fit variance given a named parameter vector as returned by the fit. fitted. pars = "missing". the fitted data. model = "character". sigma and residuals provide extractor functions for those values. uncvariance signature(object = "missing". model = "missing"): Calculates and returns the halflife of the GARCH fit variance given a uGARCHfit object. a distribution name and the GARCH model (with submodel argument for the fGARCH model). See the references in the package introduction for the original paper by Vlaar and Palm explaining the test. spec = spec) fit # object fit: slotNames(fit) # sublist fit@fit names(fit@fit) coef(fit) infocriteria(fit) likelihood(fit) nyblom(fit) signbias(fit) . The signbias methods calculates and returns the sign bias test of Engle and Ng (see the references in the package introduction). The groups parameter is a numeric vector of grouped bin sizes for the test. The news impact method returns a list with the calculated values (zx. zy) and the expression (xexpr.1]. dates). Methods for calculating and extracting persistence. Author(s) Alexios Ghalanos See Also Classes uGARCHforecast.1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[. BIC etc) of the GARCH fit.g.uGARCHfit-class 65 residuals and the sigma values. indexed (rownames) by the same values as provided in the original data provided to the fit function (e. The uncmean will only take a fit object due to the complexity of the calculation requiring much more information than the uncoditional variance. The nyblom method calculates and returns the Hansen-Nyblom joint and individual coefficient stability test statistic and critical values. unconditional variance and half-life of the GARCH shocks exist and take either the GARCH fit object as a single value otherwise you may provide a named parameter vector (see uGARCHspec section for parameter names of the various GARCH models). Examples ## Not run: # Basic GARCH(1. The uncvariance may take either a fit object or a named parameter list. uGARCHsim and uGARCHspec. The gof methods calculates and returns the adjusted goodness of fit statistic and p-values for the fitted distribution. yexpr) which can be used to illustrate the plot. Unconditional mean and variance of the model may be extracted by means of the uncmean and uncvariance methods. distribution and GARCH model name. The infocriteria method calculates and returns the information criteria (AIC. solver. Stationarity explicitly imposes the variance stationarity constraint during optimization.control = list(). ni=newsimpact(z = NULL..frame(fit)) head(sigma(fit)) head(residuals(fit)) head(fitted(fit)) gof(fit.frame. One of either “nlminb”. . matrix. Control arguments passed to the fitting routine. xlab=ni$xexpr. solver = "solnp".se = . ylab=ni$yexpr. .which="all") ugarchfit-methods # news impact example spec = ugarchspec(variance. out. A positive integer indicating the number of periods before the last to keep for out of sample forecasting (see details). main = "News Impact Curve") ## End(Not run) ugarchfit-methods function: Univariate GARCH Fitting Description Method for fitting a variety of univariate GARCH models. A univariate GARCH spec object of class uGARCHspec.. spec = spec) # note that newsimpact does not require the residuals (z) as it # will discover the relevant range to plot against by using the min/max # of the fitted residuals.. data.c(2 . The scale parameter controls whether the data should be scaled before being submitted to the optimizer. solver.1]. fixed.66 head(as.control = list(stationarity = 1.data. fit) #plot(ni$zx. . xts. scale = ). Can be a numeric vector. . type="l".control A univariate data object. fit. zoo.sample solver fit. ts or irts object.model=list(model="apARCH")) fit = ugarchfit(data = dmbp[. timeSeries..) Arguments data spec out.pars argument of the ugarchspec function). data.se argument controls whether standard errors should be calculated for those parameters which were fixed (through the fixed. “solnp” or “gosolnp”.sample = . Usage ugarchfit(spec. ni$zy.control Control arguments list passed to optimizer.5 )) uncmean(fit) uncvariance(fit) #plot(fit.3 . The fixed.4 . sample option is positive.restarts” is the number of solver restarts required (defaults to 1). In the ugarchforecast routine the n.1]. then the routine will fit only N . rolling forecast and estimation ugarchroll. “parallel” and “parallel. spec = spec) fit coef(fit) head(as. Examples # Basic GARCH(1. out.ahead may also be greater than the out. bootstrap forecast ugarchboot.out. The main part of the likelihood calculation is performed in C-code for speed. A minimum of 5 data points are required for these tests.sample number resulting in a combination of out of sample data points matched against actual data and some without. The “gosolnp” solver allows for the initialization of multiple restarts of the solnp solver with randomly generated parameters (see documentation in the Rsolnp-package for details of the strategy used). parameter distribution and uncertainty ugarchdistribution.control list then accepts the following additional (to the solnp) arguments: “n. n.which="all") # in order to use fpm (forecast performance measure function) # you need to select a subsample of the data: spec = ugarchspec() fit = ugarchfit(data = dmbp[.control” for use of the parallel functionality.sample=1 ) forc = ugarchforecast(fit.ahead=1 ) # this means that 1 data points are left from the end with which to # make inference on the forecasts fpm(forc) . If the out. Value A uGARCHfit object containing details of the GARCH fit. leaving out. which the forecast performance tests will ignore.data.1]. forecasting ugarchforecast. and “n.sim” is the number of simulated parameter vectors to generate per n.sample (where N is the total data length) data points.sample option is provided in order to carry out forecast performance testing against actual data.restarts. “rseed” is the seed to initialize the random number generator. Author(s) Alexios Ghalanos See Also For specification ugarchspec.frame(fit)) #plot(fit. simulation ugarchsim. spec = spec. The solver.1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[.filtering ugarchfilter. The out.ugarchfit-methods Details 67 The GARCH optimization routine first calculates a set of feasible starting points which are used to initiate the GARCH recursion.sample points for forecasting and testing using the forecast performance measures. frame method on the other hand provides for 5 additional arguments. The argument which indicates the type of forecast value to return(with valid valued being “sigma” and “series”). Methods as. Extends Class GARCHforecast. Depending on the intended usage of the forecasts. When “all” is chosen in the rollframe argument.roll optional argument indicating the rolling sequence to plot. directly.ahead value and row dimension 2 (sigma and series forecast).list signature(x = "uGARCHforecast"): Extracts the forecast list with all rollframes. Objects from the Class A virtual Class: No objects may be created from it. y = "missing"): Forecast plots with n. Finally.frame signature(x = "uGARCHforecast"): Extracts the forecasts. The rollframe option is for the rolling frame to return (with 0 being the default no-roll) and allows either a valid numeric value or alternatively the character value “all” for which additional options then come into play.68 uGARCHforecast-class uGARCHforecast-class class: Univariate GARCH Forecast Class Description Class for the univariate GARCH forecast. Note There are 3 main extractor functions for the uGARCHforecast object which is admittedly the most complex in the package as a result of allowing for rolling forecasts.list method works similarly returns instead a list object. as. fpm signature(object = "uGARCHforecast"): Forecast performance measures. return only those forecasts which have in sample equivalent data (value 1) or return only those values which are truly forecasts without in sample data (value 2). There are no additional arguments to these extractor functions and they will return all the forecasts. the data.array extracts an array object where each page of the array represents a roll. the type option controls whether to return all forecasts (value 0.data. as. The as.data. Class rGARCH. some or all these options may be useful to the user when extracting data from . Takes many additional arguments (see note below). The as. by class GARCHforecast. default). show signature(object = "uGARCHforecast"): Forecast summary returning the 0-roll frame only. and array dimension equal to the number of rolling forecasts chosen. plot signature(x = "uGARCHforecast". The as. distance 2.array signature(x = "uGARCHforecast"): Extracts the forecast array with matrix column dimensions equal to the n.frame returned may be time aligned (logical option aligned) in which case the logical option prepad indicates whether to pad the values prior to the forecast start time with actual values or NA (value FALSE). of rolling forecasts to create beyond the first one (see details).1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[. uGARCHsim and uGARCHspec. n.data. The no.sample = .sample . If a specification object is supplied.frame(forc)) #plot(forc. The forecast horizon. out.ugarchforecast-methods 69 the forecast object. Examples ## Not run: # Basic GARCH(1. external. data = NULL. The plot method takes additional arguments which and n. which = "all") ## End(Not run) ugarchforecast-methods function: Univariate GARCH Forecasting Description Method for forecasting from a variety of univariate GARCH models.ahead=2 ) forc head(as.1].roll = .roll out.) Arguments fitORspec Either a univariate GARCH fit object of class uGARCHfit or alternatively a univariate GARCH specification object of class uGARCHspec with valid fixed parameters.. indicates how many data points to keep for out of sample testing.ahead n. Usage ugarchforecast(fitORspec. Author(s) Alexios Ghalanos See Also Classes uGARCHfit. Optional. n. spec = spec) forc = ugarchforecast(fit. n. Required if a specification rather than a fit object is supplied.roll indicating which roll frame to plot.. data n. . vregfor = NULL).ahead = 1 .forecasts = list(mregfor = NULL. forecasts A list with forecasts for the external regressors in the mean and/or variance equations if specified. Examples ## Not run: # Basic GARCH(1. The default argument of n. Author(s) Alexios Ghalanos See Also For filtering ugarchfilter. The ability to roll the forecast 1 step at a time is implemented with the n.which="all") ## End(Not run) . since n..roll argument. or a specification object (in which case the data is required) with fixed parameters.frame(forc)) #plot(forc.ahead forecast. The forecast is based on the expected value of the innovations and hence the density chosen.1]. See the class for details on the returned object and methods for accessing it and performing some tests.ahead forecast. bootstrap forecast ugarchboot. Critically. One step ahead forecasts are based on the value of the previous data.70 ugarchforecast-methods external. Value A uGARCHforecast object containing details of the GARCH forecast.roll depends on data being available from which to base the rolling forecast. .sample being at least as large as the n.roll = 0 denotes no rolling and returns the standard n.1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[.ahead=2 ) forc head(as. n. parameter distribution and uncertainty ugarchdistribution.simulation ugarchsim..data. Details The forecast function has two dispatch methods allowing the user to call it with either a fitted object (in which case the data argument is ignored). or in the case of a specification being used instead of a fit object.sample argument directly in the forecast function. the out.roll argument which controls how many times to roll the n. the ugarchfit function needs to be called with the argument out. while n-step ahead (n>1) are based on the unconditional expectation of the models. . spec = spec) forc = ugarchforecast(fit. rolling forecast and estimation ugarchroll. Author(s) Alexios Ghalanos See Also Classes uGARCHmultiforecast. residuals signature(object = "uGARCHmultifilter"): Extracts the residuals. likelihood signature(object = "uGARCHmultifilter"): Extracts the likelihood. Methods fitted signature(object = "uGARCHmultifilter"): Extracts the fitted values. Objects from the Class A virtual Class: No objects may be created from it. uGARCHmultifit-class class: Univariate GARCH Multiple Fit Class Description Class for the univariate GARCH Multiple fit. by class GARCHfit. Class rGARCH. directly. Extends Class "GARCHfilter". sigma signature(object = "uGARCHmultifilter"): Extracts the conditional sigma values. show signature(object = "uGARCHmultifilter"): Filter summary. directly. distance 3. by class "GARCHfilter". Extends Class GARCHfit. . uGARCHmultifit and uGARCHmultispec. distance 3.uGARCHmultifilter-class 71 uGARCHmultifilter-class class: Univariate GARCH Multiple Filter Class Description Class for the univariate GARCH Multiple filter. Class "rGARCH". coef signature(object = "uGARCHmultifilter"): Extracts the coefficients. . The optional argument “which” allows to choose from “sigma” and “series” to return the forecasts for. fitted signature(object = "uGARCHmultifit"): Extracts the fitted values. Author(s) Alexios Ghalanos See Also Classes uGARCHmultiforecast. sigma and residuals provide extractor functions for those values. Note Methods for coef. fitted. sigma signature(object = "uGARCHmultifit"): Extracts the conditional sigma values.roll. uGARCHmultiforecast-class class: Univariate GARCH Multiple Forecast Class Description Class for the univariate GARCH Multiple forecast. likelihood signature(object = "uGARCHmultifit"): Extracts the likelihood.array signature(x = "uGARCHmultiforecast"): extracts the forecast array with matrix column dimensions equal to the number of assets. residuals signature(object = "uGARCHmultifit"): Extracts the residuals. Objects from the Class A virtual Class: No objects may be created from it. sublists equal to n. distance 3.72 Methods uGARCHmultiforecast-class coef signature(object = "uGARCHmultifit"): Extracts the coefficients. uGARCHmultispec and uGARCHmultifilter. Methods as. directly. Class rGARCH.ahead and array dimension equal to the number of rolling forecasts chosen. show signature(object = "uGARCHforecast"): forecast summary. likelihood. show signature(object = "uGARCHmultifit"): Fit summary.list signature(x = "uGARCHforecast"): extracts the forecast list of length equal to the number of assets. Extends Class GARCHforecast. as. row dimension of each sublist equal to n. by class GARCHforecast. row dimension the n.ahead and column dimension equal to 2 (sigma and series forecasts). Objects from the Class A virtual Class: No objects may be created from it. Methods show signature(object = "uGARCHmultispec"): specification summary. by class "GARCHspec". uGARCHmultispec-class class: Univariate GARCH Multiple Specification Class Description Class for the univariate GARCH Multiple specification. . uGARCHmultifit and uGARCHmultifilter. Extends Class "GARCHspec".uGARCHmultispec-class Author(s) Alexios Ghalanos 73 See Also Classes uGARCHmultifilter. directly. Author(s) Alexios Ghalanos See Also Classes uGARCHmultiforecast. Class "rGARCH". uGARCHmultifit and uGARCHmultispec. distance 3. . The dimension of the data. “series” for the simulated series and “residuals” for the simulated residuals.sim by m. Class "rGARCH".frame function takes optionally 1 additional arguments. uGARCHfit and uGARCHspec. by class "GARCHpath". indicating the type of simulation path series to extract. Methods as.74 uGARCHpath-class uGARCHpath-class class: Univariate GARCH Path Simulation Class Description Class for the univariate GARCH Path simulation. Extends Class "uGARCHpath". Valid values are “sigma” for the simulated sigma. namely which.sim. Author(s) Alexios Ghalanos See Also Classes uGARCHsim. distance 2.data. y = "missing"): path simulation plots.frame will be n. directly. show signature(object = "uGARCHpath"): path simulation summary.frame signature(x = "uGARCHpath"): extracts the simulated path values (see note). Note The as. Objects from the Class A virtual Class: No objects may be created from it. plot signature(x = "uGARCHpath".data. with each matrix having n. For m. prereturns=NA. it is possible to provide either a single seed to initialize all values.. mexsimdata=NULL.sim n. with each matrix having n.e. m.) Arguments spec A univariate GARCH spec object of class uGARCHspec with the required parameters of the model supplied via the fixed. preresiduals=NA. or one seed per separate simulation (i. n. n.sim>1.start m. This is a convenience function which does not require a fitted object (see note below).distfit=NA). The simulation horizon.sim is. m.sim=1.start= . Optional seeding value(s) for the random number generator.pars list argument or setfixed<method. presigma=NA. Allows the starting residuals to be provided by the user..dist=list(name=NA. List of matrices (size of list m.. n. If the fit object contains external regressors in the mean equation.ugarchpath-methods 75 ugarchpath-methods function: Univariate GARCH Path Simulation Description Method for simulating the path of a GARCH model from a variety of univariate GARCH models. . Optional density with fitted object from which to simulate. The burn-in sample.sim rows) of simulated external regressor-in-variance data. Usage ugarchpath(spec. If the fit object contains external regressors in the mean equation.dist mexsimdata vexsimdata . The number of simulations. custom. in the latter case this may result in some slight overhead depending on how large m.sim. this must be provided else will be assumed zero.. However.sim.sim rows) of simulated external regressor-in-mean data. Allows the starting sigma values to be provided by the user. . List of matrices (size of list m. Allows the starting return data to be provided by the user.sim seeds). rseed=NA.sim presigma prereturns preresiduals rseed custom. this must be provided else will be assumed zero. See notes below for details. . vexsimdata=NULL.sim=1 . garchInMean = FALSE. alpha1= .model=list(model="sGARCH".sim=1) ## End(Not run) uGARCHroll-class class: Univariate GARCH Rolling Forecast Class Description Class for the univariate GARCH rolling forecast.76 Details uGARCHroll-class This is a convenience method to allow path simulation of various GARCH models without the need to supply a fit object as in the ugarchsim method.1)).9 . filtering ugarchfilter. n. fitting ugarchfit. .model="sstd". fixed.sgarch = ugarchpath(spec. mean. distance 2. ). beta1= . Extends Class "GARCHroll".pars=list(mu= . shape=4. 5. 1. inMeanType = 2). Objects from the Class A virtual Class: No objects may be created from it. Value A uGARCHpath object containing details of the GARCH path simulation. include.skew=2)) # simulate the path path. rolling forecast and estimation ugarchroll.sim=3 . by class "GARCHroll".omega= . forecasting ugarchforecast. directly. simulation ugarchsim.start=1. parameter distribution and uncertainty ugarchdistribution. bootstrap forecast ugarchboot.model=list(armaOrder=c( . Instead. n.mean=TRUE. Examples ## Not run: # create a basic sGARCH(1. distribution. garchOrder=c(1. 1.1) spec: spec=ugarchspec(variance. a GARCH spec object is required with the fixed model parameters. Class "rGARCH". Author(s) Alexios Ghalanos See Also For specification ugarchspec. m. ahead for the n.01. VaR.data. Additionally. this is the tail probability and defaults to 0.95). else will default to “ask” for interactive printing of the options in the command windows. plot signature(x = "uGARCHroll". density.alpha for the Value at Risk backtest plot. Valid values are “coefs” returning the parameter coefficients for all refits.ahead for the rolling n. refit indicates which refit window to return the “coefmat” if that was chosen. the value of “all” wil create a 2x2 chart with all plots.01. Author(s) Alexios Ghalanos . n.level the confidence level upon which the conditional coverage hypothesis test will be based on (defaults to 0. report signature(object = "uGARCHroll"): Roll backtest reports (see note).frame extractor method allows the extraction of a variety of values from the object. as.uGARCHforecast signature(object = "uGARCHroll"): Extracts and converts the forecast object contained in the roll object to one of uGARCHforecast given the refit number supplied by additional argument ‘refit’ (defaults to 1). The report method takes the following additional arguments: type for the report type.15) but you should change this to something more appropriate for your data and period under consideration.ahead forecasts (defaults to 1). n. and “VaR” for the Value At Risk measure if it was requested in the roll function call. n.ahead forecasts (defaults to 1).data. fpm signature(object = "uGARCHroll"): Forecast performance measures. y = "missing"): Roll result backtest plots (see note). defaults to c(-0. Valid values are “VaR” for the Value at Risk report based on the unconditional and conditional coverage tests for VaR exceedances (discussed below) and “fpm” for forecast performance measures.values.alpha for the Value at Risk backtest report. Note The as. Both the joint and the separate unconditional test are reported since it is always possible that the joint test passes while failing either the independence or unconditional coverage test. Additional arguments are: which indicates the type of value to return. while the conditional coverage test of Christoffersen is a joint test of the unconditional coverage and the independence of the exceedances. 0. show signature(object = "uGARCHroll"): Summary. “coefmat” for the parameter coefficients with their respective standard errors and t. conf.15. Kupiec’s unconditional coverage test looks at whether the amount of expected versus actual exceedances given the tail probability of VaR actually occur as predicted. this is the tail probability and defaults to 0. “LLH” for the likelihood across the refits.ahead for the rolling n.and p. “density” for the parametric density.ahead forecast horizon to return if which was used with arguments “density” or “VaR”.support the support for the time varying density plot density.uGARCHroll-class Methods 77 as.frame signature(x = "uGARCHroll"): Extracts various values from object (see note). The plot method takes the following additional arguments: which allows for either a numeric value of 1:4. VaR. fit. .alpha ..window Determines every how many periods the model is re-estimated. 5).every = 25. VaR. and the number of cores to make use of. parallel.VaR VaR. A univariate dataset.) Arguments spec data n. "moving"). Whether to calculate forecast Value at Risk during the estimation. . data. calculate. solver.. Usage ugarchroll(spec. .control = list(). The number of periods to forecast.ahead forecast. parallel parallel. "snowfall"). solver fit.78 ugarchroll-methods ugarchroll-methods function: Univariate GARCH Rolling Density Forecast and Backtesting Description Method for creating rolling density forecast from ARMA-GARCH models with option for refitting every n periods and some multicore parallel functionality. parallel = FALSE. Whether to make use of parallel processing on multicore systems.length The length of the total forecast for which out of sample data from the dataset will be excluded for testing.VaR = TRUE. .ahead = 1. cores = 2). refit. 1.control = list(pkg = c("multicore". calculate. Whether the refit is done on an expanding window including all the previous data or a moving window. refit. the length of the window determined by the argument above (“refit..control Control parameters passed to the solver. The Value at Risk tail level to calculate.. solver.control = list(). refit.control The solver to use. A univariate GARCH spec object specifiying the desired model for testing. forecast.alpha = c( .window = c("recursive". n.length = 5 . solver = "solnp". Control parameters parameters passed to the fitting function.every”).control The parallel control options including the type of package for performing the parallel calculations (‘multicore’ for non-windows O/S and ‘snowfall’ for all O/S).every refit. The important thing to remember about the refit.control = list().ugarchroll-methods Details 79 GARCH models generate a partially time varying density based on the variation in the conditional sigma and mean values (skewness and shape are usually not time varying in GARCH models unless the underlying distribution has an interaction with the conditional sigma).model = list(model = "sGARCH".model = "std") sp5 . For example for n. For example. However. filtering ugarchfilter. for a refit. skew. tol = 1e-7) spec = ugarchspec(variance. forecast. the user can calculate many others (see for example partial moments based measures or the PedersenSatchell family of measures).every of 25. outer. Author(s) Alexios Ghalanos See Also For specification ugarchspec. delta = 1e-9.bktest = ugarchroll(spec. garchOrder = c(1. we take the floor of the division of 500 by 30 which is 16 windows of 30 periods each for a total actual forecast length of 480 (16 x 30).every of 30.every of 25. Examples ## Not run: data(sp5 ret) ctrl = list(rho = 1.ahead of 1 and refit. for a forecast length of 500 and refit.iter = 1 .every = 25. simulation ugarchsim. sigma. n.forecast is 500)! The function has 2 main methods for viewing the data.every of 1 we will get 1 n. shape).every is that it acts like the n. the forecast is rolled every day using the filtered (actual) data of the previous period while for n.1)). shape) to the one representing the underlying return process (mu. forecasting ugarchforecast. refit. The function first generates rolling forecasts of the ARMA-GARCH model and then rescales the density from a standardized (0.window = "recursive".mean = TRUE). bootstrap forecast ugarchboot. this is 20 windows of 25 periods each for a total actual forecast length of 500.every determines every how many periods the fit is recalculated and the total forecast length actually calculated. solver. solver = "solnp".ahead of 1 and refit.ahead forecasts for every day after which the model is refitted and reforecast for a total of 500 refits (when length. a standard plot method and a new report methods (see class uGARCHroll for details on how to use these methods). ). skew. The argument refit. 1. parameter distribution and uncertainty ugarchdistribution. mean. data = sp5 ret. include. Value An object of class uGARCHroll. but since the full time varying density parameters are returned. . distribution.roll argument in the ugarchforecast function as it determines the number of rolls to perform. fitting ugarchfit.control = ctrl. The function calculates one such measure (VaR).ahead = 1. fit.length = 1 . refit. Given this information it is then a simple matter to generate any measure of risk through the analytical evaluation of some type of function of the time varying density.model = list(armaOrder = c( . 1. indicating the type of simulation series to extract. directly. Methods as. type="fpm") ## End(Not run) uGARCHsim-class . uGARCHfit and uGARCHspec. . 5)) report(sp5 . type="VaR". model: Object of class "vector" The model specification common to all objects.sim by m.level = .bktest. The dimension of the data.frame signature(x = "uGARCHsim"): Extracts the simulated values (see note). VaR.alpha = conf. n. uGARCHsim-class class: Univariate GARCH Simulation Class Description Class for the univariate GARCH simulation. namely which. . Extends Class "GARCHsim". VaR. Class "rGARCH".bktest. Valid values are “sigma” for the simulated sigma. “series” for the simulated series and “residuals” for the simulated residuals.data. distance 2.frame function takes optionally 1 additional arguments. .alpha = c( .data.80 calculate. Slots simulation: Object of class "vector" Holds data on the simulation.frame will be n.sim. by class "GARCHsim". y = "missing"): Simulation plots. Author(s) Alexios Ghalanos See Also Classes uGARCHforecast. seed: Object of class "integer" The random seed used. 25. 1.95) report(sp5 . Note The as.ahead = 1.VaR = TRUE. show signature(object = "uGARCHsim"): Simulation summary. plot signature(x = "uGARCHsim". ) Arguments fit n. presigma = NA.start m. and “sample” for the ending values of the actual data from the fit object. Valid methods are “unconditional” for the expected values given the density.sim = 1 . prereturns = NA. mexsimdata = NULL. m.sim>1. which = "sigma")) ## End(Not run) 81 ugarchsim-methods function: Univariate GARCH Simulation Description Method for simulation from a variety of univariate GARCH models. distfit = NA). startMethod="sample") sim # plot(sim. However. m. Optional seeding value(s) for the random number generator.sim=1 . n. The simulation horizon. startMethod = c("unconditional". For m.ugarchsim-methods Examples ## Not run: # Basic GARCH(1. Starting values for the simulation. The number of simulations.sim seeds).. or one seed per separate simulation (i. presigma prereturns preresiduals rseed . spec = spec) sim = ugarchsim(fit. in the latter case this may result in some slight overhead depending on how large m. preresiduals = NA. which="all") # as. Usage ugarchsim(fit. rseed = NA. n.sim is.sim = 1.e.dist = list(name = NA.data. n.start = .. it is possible to provide either a single seed to initialize all values. The burn-in sample. m. Allows the starting return data to be provided by the user. custom.data.1]. Allows the starting sigma values to be provided by the user.n. "series" and "residuals" head(as.start=1.sim n.sim=1. .frame(sim.1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[. Allows the starting residuals to be provided by the user.sim startMethod A univariate GARCH fit object of class uGARCHfit. "sample").frame takes an extra argument which # indicating one of "sigma". vexsimdata = NULL. spec = spec) sim = ugarchsim(fit.sim rows) of simulated external regressor-in-mean data.dist can take any name in the name slot (e. which="all") # as..1) Spec data(dmbp) spec = ugarchspec() fit = ugarchfit(data = dmbp[. filtering ugarchfilter.g.start=1. rnorm) and “d” (density e. If the fit object contains external regressors in the mean equation. with each matrix having n. with each matrix having n.“sample”) and a matrix in the fit slot with dimensions equal to m. which = "sigma")) .dist mexsimdata ugarchsim-methods Optional density with fitted object from which to simulate.data.frame takes an extra argument which # indicating one of "sigma".sim (columns) and n.sim=1 . n.. fitting ugarchfit.g. It must take a single fit object as its second argument. Examples ## Not run: # Basic GARCH(1. Details The custom. List of matrices (size of list m. dnorm).sim.dist option allows for defining a custom density which exists in the users workspace with methods for “r” (sampling. m.frame(sim.sim=1. e. Alternatively. If the fit object contains external regressors in the mean equation.sim (rows).sim rows) of simulated external regressor-in-variance data. forecasting ugarchforecast. rolling forecast and estimation ugarchroll. parameter distribution and uncertainty ugarchdistribution.1]. bootstrap forecast ugarchboot. "series" and "residuals" head(as.n. this must be provided else will be assumed zero. this must be provided else will be assumed zero.g. See notes below for details.data.sim. The usefulness of this becomes apparent when one is considering the copula-GARCH approach or the bootstrap method. Author(s) Alexios Ghalanos See Also For specification ugarchspec. . List of matrices (size of list m. custom. Value A uGARCHsim object containing details of the GARCH simulation.82 custom. vexsimdata . startMethod="sample") sim # plot(sim. distance 2. value = "vector"): Sets the fixed parameters (which must be supplied as a named list). uncmean signature(object = "uGARCHspec"): Unconditional mean of model for a specification with fixed. halflife signature(object = "uGARCHspec".signature(object = "uGARCHspec". Slots model: Object of class "vector" The model specification common to all objects. distribution = "missing". pars = "missing". Methods show signature(object = "uGARCHspec"): Specification summary. Author(s) Alexios Ghalanos See Also Classes uGARCHfit. model = "missing". persistence signature(object = "uGARCHfit". . submodel = "missing". model = "missing"): Calculates and returns the halflife of the GARCH fit variance given a uGARCHspec object with fixed parameters. Extends Class "GARCHspec". vexdata = "missing"): Calculates and returns the long run unconditional variance of the GARCH fit given a uGARCHfit object. distribution = "missing". by class "GARCHspec". pars = "missing". pars = "missing".uGARCHspec-class ## End(Not run) 83 uGARCHspec-class class: Univariate GARCH Specification Class Description Class for the univariate GARCH specification. Class "rGARCH". model = "missing"): Calculates and returns the persistence of the GARCH fit model given a uGARCHspec object with fixed parameters. value = "vector"): Sets the starting parameters (which must be supplied as a named list). setstart<.pars list.pars list. setfixed<. directly. distribution = "missing". uGARCHsim and uGARCHforecast.signature(object = "uGARCHspec". uncvariance signature(object = "uGARCHspec"): Unconditional variance of model for a specification with fixed. uncvariance signature(object = "uGARCHspec". regressors = NULL. mean. variance. “NGARCH”. submodel = NULL. distribution.. garchOrder = c(1.84 Examples # Basic GARCH(1. 1).deviation (1) or variance (2) in the ARCH in mean regression. garchOrder The ARCH (q) and GARCH (p) orders. arfima = FALSE. external. “apARCH” and “iGARCH”. valid submodels are “GARCH”.model List containing the mean model specification: armaOrder The autoregressive (ar) and moving average (ma) orders (if any).targeting = FALSE).pars = list().targeting Indicates whether to use variance targeting for the sigma intercept “omega”. .1) Spec spec = ugarchspec() spec ugarchspec-methods ugarchspec-methods function: Univariate GARCH Specification Description Method for creating a univariate GARCH specification object prior to fitting. “eGARCH”. archex = FALSE). submodel If the model is “fGARCH”.model = "norm". Usage ugarchspec(variance. start. “fGARCH”.regressors A matrix object containing the external regressors to include in the mean equation with as many rows as will be included in the data (which is passed in the fit function).) Arguments variance. variance.model = list(armaOrder = c(1. include.regressors = NULL. 1). arfima Whether to fractional differencing in the ARMA regression. external. “NAGARCH”. .). archm Whether to include ARCH volatility in the mean regression. external.“GJRGARCH” and “ALLGARCH”.model List containing the variance model specification: model Valid models (currently implemented) are “sGARCH”. external. archpow Indicates whether to use st. “APARCH”..pars = list(). “gjrGARCH”. mean. include. fixed. “TGARCH”.regressors A matrix object containing the external regressors to include in the variance equation with as many rows as will be included in the data (which is passed in the fit function). archpow = 1.model = list(model = "sGARCH". archex (integer) Whether to multiply the last ’archex’ external regressors by the conditional standard deviation.mean = TRUE.mean Whether to include the mean. archm = FALSE. “AVGARCH”. In order to understand which parameters can be entered in the start. The “jsu” distribution is the reparametrized version from the “gamlss” package. It is possible that you designate all parameters as fixed so as to quickly recover just the results of some previous work or published work. The asymmetry term in the rugarch package. “ghyp” for the Generalized Hyperbolic. ARFIMAX is fully supported in fitting. forecasting and simulation.ugarchspec-methods 85 distribution.model The conditional density to use for the innovations.se” in the ugarchfit function indicates whether to calculate standard errors for those parameters fixed during the post optimization stage. referred to in Engle and Mezrich (1996). for all implemented models. “ged” for the generalized error distribution. List of parameters which are to be kept fixed during the optimization. . For the “EWMA” model just set “omega” to zero in the fixed parameters list. and mean equation modelling.pars List of staring parameters for the optimization routine. For the “fGARCH” model.. the sample average of the external regresssors is multiplied by their coefficient and subtracted from the variance target.pars optional arguments. this represents the order of the model. Note that some of the distributions are taken from the fBasics package and implenented locally here for convenience. which may be of use for example in calculating the correlation coefficient in a CAPM type setting.pars fixed. and “jsu” for Johnson’s SU distribution. the list below exposes the names used for the parameters across the various models:(note that when a parameter is followed by a number. For the mean equation. “sged” for the skew-generalized error distribution. There is also an option to multiply the external regressors by the conditional standard deviation. Details The specification allows for a wide choice in univariate GARCH models. this represents Hentschel’s omnibus model which subsumes many others. “nig” for the normal inverse gaussian distribution. replaces the intercept “omega” in the variance equation by 1 minus the persistence multiplied by the unconditional variance which is calculated by its sample counterpart in the squared residuals during estimation. The optional argument “fixed. “std” for the student-t. follows the order of the arch parameter alpha. Variance targeting. The “iGARCH” implements the integrated GARCH model. In the presence of external regressors in the variance equation. “snorm” for the skew-normal distribution. Just increment the number for higher orders): Mean Model: constant AR term MA term ARCH in mean exogenous regressors arfima mu ar1 ma1 archm mxreg1 arfima . distributions. . “sstd” for the skew-student.. start. These are not usually required unless the optimization has problems converging.pars and fixed. Valid choices are “norm” for the normal distibution. EGARCH): assymetry term gamma1 Variance Model (APARCH): assymetry term power term gamma1 delta Variance Model (FGARCH): assymetry term1 (rotation) assymetry term2 (shift) power term1(shock) power term2(variance) eta11 eta21 delta lambda Value A uGARCHspec object containing details of the GARCH specification.86 Distribution Model: ghlambda skew shape lambda (for GHYP distribution) skew shape ugarchspec-methods Variance Model (common specs): constant ARCH term GARCH term exogenous regressors omega alpha1 beta1 vxreg1 Variance Model (GJR. Author(s) Alexios Ghalanos . The format of the dates e. day of the week variable given a set of dates.1)).ma1= . fixed.mean=TRUE). Character string indicating day of week. Usage WeekDayDummy(Dates. garchOrder=c(1.pars=list(omega= )) 87 WeekDayDummy-methods function: Create Dummy Day-of-Week Variable Description Helper function to create a dummy.model=list(armaOrder=c(2. weekday = "Monday") Arguments Dates date.format weekday Value A numeric vector of 0s and 1s (date-dummy variable)/ Author(s) Alexios Ghalanos Examples data(sp5 ret) Dates=rownames(sp5 ret) # create Monday dummy monday=WeekDayDummy(Dates. distribution. ).3))) spec2 # an example of the EWMA Model spec3 = ugarchspec(variance.g.format="%Y-%m-%d".model=list(model="iGARCH". date.3. .WeekDayDummy-methods Examples # a standard specification spec1 = ugarchspec() spec1 # an example which keep the ar1 and ma1 coefficients fixed: spec2 = ugarchspec(mean.pars=list(ar1= .model="norm". date. fixed. “%Y-%m-%d"” . weekday = "Monday") A character vector of dates .2).format. include.model=list(armaOrder=c( . mean. ARFIMAspec-method (arfimadistribution-methods). 39 GARCHfilter-class. 10. 41 GARCHpath-class. 42 GARCHroll-class. 83 ∗Topic datasets 88 dji3 ret. 7 arfimadistribution-methods. 52 ∗Topic methods arfimadistribution-methods. 72 uGARCHmultispec-class. 7 arfimadistribution (arfimadistribution-methods). 30 GARCHboot-class. 48 multispec-methods. 24 ARFIMAroll-class.Index ∗Topic classes ARFIMA-class. 74 uGARCHroll-class.ANY-method (arfimadistribution-methods). 22–24. 13 ARFIMAforecast-class. 37 sp5 ret. 84 WeekDayDummy-methods. 7. 6 ARFIMAdistribution. 26 ARFIMAsim-class. 71 uGARCHmultifit-class. 31 ARFIMA-class. 8 arfimafilter-methods. 17. 22 ARFIMAmultiforecast-class. 60 uGARCHfit-class. 66 ugarchforecast-methods. 37 multifit-methods. 81 ugarchspec-methods. 8 arfimadistribution. 47 multiforecast-methods. 75 ugarchroll-methods. 43 GARCHspec-class. 68 uGARCHmultifilter-class. 57 uGARCHfilter-class. 80 uGARCHspec-class. 8 ARFIMAdistribution-class. 8 . 14 arfimaforecast-methods.ARFIMAfit-method (arfimadistribution-methods). 7 ARFIMAfilter-class. 8 arfimadistribution. 54 uGARCHdistribution-class. 10 ARFIMAfit-class. 58 ugarchfit-methods. 71 uGARCHmultiforecast-class. 27 arfimasim-methods. 26. 11 arfimafit-methods. 50 uGARCHboot-class. 40 GARCHfit-class. 6 ARFIMAdistribution-class. 14. 36 dmbp. 29 arfimaspec-methods. 8 arfimadistribution. 78 ugarchsim-methods. 69 ugarchpath-methods. 29. 44 rGARCH-class. 73 uGARCHpath-class. 31 ForwardDates-methods. 44 GARCHtests-class. 38 GARCHdistribution-class. 23 ARFIMApath-class. 40 GARCHforecast-class. 9 arfimadistribution. 25 arfimaroll-methods. 29 ARFIMAspec-class. 18 arfimapath-methods. 42 GARCHsim-class. 63 uGARCHforecast-class. 76 uGARCHsim-class. 49 ugarchboot-methods. 55 ugarchdistribution-methods. 21 ARFIMAmultifit-class. 87 ARFIMA. 17 ARFIMAmultifilter-class. 23 ARFIMAmultispec-class. 18 arfimaforecast.ARFIMAforecast.array. 49 ARFIMAmultiforecast-class. 11.ARFIMAforecast-method (ARFIMAforecast-class). 49 arfimaspec.data. 30 arfimafit. 15. 25 arfimapath.data. 14 ARFIMAfit-class. 18.array. 26 arfimaroll-methods. 17 arfimaforecast-methods.ARFIMAforecast (ARFIMAroll-class). 25 arfimasim (arfimasim-methods). 25 arfimapath.ARFIMAspec-method (arfimafilter-methods). 26 as. 14 arfimafit. 23 ARFIMAmultispec. 28 arfimaforecast (arfimaforecast-methods). 14 arfimafit. 18. 30 arfimaspec-methods. 72 as.ARFIMAspec-method (arfimaforecast-methods). 46–49 ARFIMAmultispec-class.ARFIMAroll-method (ARFIMAroll-class). 21 ARFIMAmultifit. 18.ANY-method (arfimaforecast-methods). 24 as. 15. 11 ARFIMAfit. 8.data.frame. 25 arfimapath (arfimapath-methods). 15. 29 arfimasim. 26 as. 14 ARFIMAforecast.ANY-method (arfimafit-methods). 8.ARFIMAspec-method (arfimafit-methods). 29 ARFIMAspec.frame.ARFIMAfilter-method (ARFIMAfilter-class).frame.ARFIMAspec-method (arfimaroll-methods). 29 arfimasim.data. 47 arfimaspec (arfimaspec-methods). 10 arfimafilter-methods.frame. 46–48 ARFIMAmultifit-class.array. 17 as. 17 as. 28 arfimaroll (arfimaroll-methods).ARFIMAroll-method (ARFIMAroll-class). 11 arfimafilter.ANY-method (ARFIMAroll-class). 24 arfimapath-methods.ANY-method (arfimafilter-methods). 31 as.uGARCHforecast-method (uGARCHforecast-class).ANY-method (arfimaspec-methods).frame.data. 32 arfimafit (arfimafit-methods). 29 . 25 ARFIMAroll. 68 as. 25.ARFIMAdistribution-method (ARFIMAdistribution-class). 11.frame. 13 as. 22 ARFIMAmultiforecast.ARFIMAforecast.ARFIMApath-method (ARFIMApath-class). 18 ARFIMAmultifilter. 27 ARFIMAroll-class. 29 ARFIMAsim-class. 18 arfimaforecast. 7 as. 10 as. 27 arfimaroll. 15. 11 arfimafilter.ARFIMAsim-method (ARFIMAsim-class). 29 arfimasim-methods.frame. 32.ARFIMAforecast-method (ARFIMAforecast-class).ANY-method (arfimasim-methods).ARFIMAfit-method (arfimasim-methods). 18 ARFIMAforecast-class. 30 arfimasim. 18 arfimaforecast. 25 ARFIMApath-class. 27 ARFIMAsim. 19.data.ANY-method 89 (arfimaroll-methods). 12 arfimafilter (arfimafilter-methods).ARFIMAmultiforecast-method (ARFIMAmultiforecast-class). 31 ARFIMAspec-class.array. 11 ARFIMAfilter-class. 26 as.ARFIMAfit-method (ARFIMAfit-class).INDEX ARFIMAfilter. 26 as.uGARCHmultiforecast-method (uGARCHmultiforecast-class). 27 arfimaroll. 13 arfimafit-methods.ANY-method (arfimapath-methods). 31 arfimaspec.ARFIMAspec-method (arfimapath-methods). 26 arfimaforecast. 23 ARFIMApath.ARFIMAfit-method (arfimaforecast-methods). 46 ARFIMAmultifilter-class.data. 23 as. data.uGARCHforecast (uGARCHroll-class).frame.uGARCHmultifit-method (uGARCHmultifit-class). 68 as.uGARCHroll-method (uGARCHroll-class).uGARCHfilter-method (uGARCHfilter-class).data.ARFIMAfilter-method (ARFIMAfilter-class). 5 ddist (rgarchdist).frame. 74 as. 60 fitted.90 as.uGARCHforecast. 10 fitted.uGARCHmultifit-method (uGARCHmultifit-class). 10 coef.ANY-method (uGARCHforecast-class).ARFIMAfilter-method (ARFIMAfilter-class). 50 INDEX fitdist (rgarchdist). 5 ForwardDates (ForwardDates-methods).ARFIMAforecast-method (ARFIMAforecast-class).frame. 80 as. 71 fitted.uGARCHfit-method (uGARCHfit-class).uGARCHfit-method (uGARCHfit-class). 37 ForwardDates-method (ForwardDates-methods). 71 coef. 60 as. 57 as. 23 as. 71 convergence (uGARCHfit-class).data. 22 fitted.uGARCHfilter-method (uGARCHfilter-class).data.uGARCHmultiforecast-method (uGARCHmultiforecast-class). 22 coef. 37 fpm (uGARCHforecast-class). 50 dji3 ret.list.data.uGARCHforecast-method (uGARCHforecast-class). 63 fitted. 17 fpm.uGARCHforecast.uGARCHsim-method (uGARCHsim-class).data. 37 ForwardDates. 68 . 71 ForwardDates.uGARCHpath-method (uGARCHpath-class). 37 ForwardDates. 33 coef.uGARCHforecast-method (uGARCHforecast-class).ARFIMAmultiforecast-method (ARFIMAmultiforecast-class). 17 as.uGARCHforecast-method (uGARCHforecast-class).list.frame.ARFIMAforecast-method (ARFIMAforecast-class).ARFIMAmultifilter-method (ARFIMAmultifilter-class). 26 fpm. 76 as.uGARCHboot-method (uGARCHboot-class). 13 coef.ANY-method (uGARCHroll-class). 21 coef. 50 dmbp.list.ARFIMAfit-method (ARFIMAfit-class). 50 fitted.uGARCHfilter-method (uGARCHfilter-class).uGARCHfit-method (uGARCHfit-class).data.ARFIMAmultifit-method (ARFIMAmultifit-class).frame.ARFIMAmultifilter-method (ARFIMAmultifilter-class). 21 fitted. 63 DACTest. 68 fpm. 76 as. 76 BerkowitzLR. 63 as.uGARCHroll-method (uGARCHroll-class). 63 coef. 54 as.data.uGARCHmultifilter-method (uGARCHmultifilter-class).ARFIMAfit-method (ARFIMAfit-class). 35 Date. 13 fitted.uGARCHmultifilter-method (uGARCHmultifilter-class). 72 as.uGARCHfit-method (uGARCHfit-class).frame. 60 coef. 63 convergence.frame.ANY-method (ForwardDates-methods). 76 as.frame. 37 dskewness (rgarchdist).list. 37 ForwardDates-methods. 68 fpm. 68 as. 63 convergence.character-method (ForwardDates-methods).uGARCHdistribution-method (uGARCHdistribution-class). 36 dkurtosis (rgarchdist).ARFIMAmultifit-method (ARFIMAmultifit-class).ARFIMAroll-method (ARFIMAroll-class).ANY-method (uGARCHfit-class). 71 likelihood. 63 likelihood (uGARCHfit-class). 46 (uGARCHfit-class).numeric-method (uGARCHfit-class).uGARCHfit.INDEX fpm. 71 91 multifilter. 63 ghyptransform. 63 multifilter. 60 likelihood.ANY.ARFIMAfilter-method (ARFIMAfilter-class).missing.missing. 63 likelihood. 57 GARCHdistribution-class. 83 multifit (multifit-methods). 46 multifilter.ANY-method (uGARCHfit-class).ANY-method (multifit-methods).ANY. 38 GARCHdistribution. 42 GARCHsim. 72 GARCHforecast-class. 71 GARCHfilter-class.ANY.uGARCHspec. 63 likelihood. 46 (uGARCHfilter-class).uGARCHmultifit-method (uGARCHmultifit-class). 22 likelihood.ARFIMAmultifilter-method (ARFIMAmultifilter-class). 46 (uGARCHfit-class). 63 gof. 63 multifilter. 21 likelihood. 40 GARCHforecast.missing.ARFIMAfit-method (ARFIMAfit-class). 46 halflife (uGARCHfit-class). 60.ANY-method (uGARCHfit-class).uGARCHfilter-method (uGARCHfilter-class). 68.missing. 47 multifit. 43 GARCHspec. 63 getspec.uGARCHfilter-method (uGARCHfilter-class).uGARCHfilter.character. 40 GARCHfit. 63 multifilter-methods.ARFIMAfit-method (ARFIMAfit-class).numeric.uGARCHfilter. 80 GARCHsim-class. 39 GARCHfilter. 60 multifilter. 63. 63 multifilter.uGARCHmultifit-method halflife. 41 GARCHpath-class. 54 GARCHboot-class. 76 GARCHboot. 63 47 . 76 GARCHroll-class. 13 infocriteria.missing.ANY. 60 infocriteria. 46 halflife.uGARCHfit-method (uGARCHfit-class). 44 GARCHtests-class.missing. 63 getspec. 10 infocriteria.missing.missing. 4 (uGARCHspec-class).missing-method multifit. 10 likelihood. 44 getspec (uGARCHfit-class).missing. 4 multifilter (multifilter-methods). 4.missing-method (multifilter-methods).uGARCHmultifilter-method (uGARCHmultifilter-class). infocriteria (uGARCHfit-class). 42 GARCHroll.ARFIMAmultispec-method halflife.ANY-method (multifilter-methods).ANY-method (multifilter-methods). 46 (uGARCHfit-class). 73.uGARCHmultispec-method halflife.ANY-method (multifilter-methods).missing-method (multifilter-methods).character.ARFIMAfilter-method (ARFIMAfilter-class).ANY-method (uGARCHfit-class).ARFIMAfit-method (ARFIMAfit-class). 13 getspec. 63 gof. 45 gof (uGARCHfit-class). 60 gof.ARFIMAmultifit-method halflife.ANY.missing. 63 infocriteria. 63 infocriteria. 71 GARCHfit-class.uGARCHfit. 83 GARCHspec-class.uGARCHfit-method (uGARCHfit-class). 63 likelihood.ARFIMAmultifit-method (ARFIMAmultifit-class). 13 likelihood.uGARCHfit-method (uGARCHfit-class).uGARCHroll-method (uGARCHroll-class).ANY-method (uGARCHfit-class).numeric-method (uGARCHfilter-class). missing-method 60.ANY-method residuals. 74 plot. 47 multifit-methods. 49 multispec-methods. 48 multiforecast.uGARCHmultifit-method (multiforecast-methods).ANY-method rGARCH.uGARCHpath.uGARCHspec.ARFIMAmultifit-method nyblom (uGARCHfit-class).uGARCHfilter. 83 plot. 10.uGARCHfit.missing. 48 multiforecast. 6.missing-met (uGARCHspec-class). 76 report.uGARCHfit. 76 plot. 54.ARFIMAmultifit-method (multiforecast-methods). 63 residuals. 50 residuals. 83 (uGARCHfilter-class). 49 multispec.vector-method (multispec-methods). 26 report.missing-method (uGARCHpath-class). 57 plot. persistence. 63 (uGARCHmultifit-class).missing. 17.character. 68.uGARCHsim. 63 rgarchdist. 14. 63 residuals. 48 multiforecast.ANY. 76 report.missing-method (uGARCHboot-class). 48 multiforecast. 63 39–44.missing.missing-method (uGARCHforecast-class). 60 plot.uGARCHfit-method (uGARCHfit-class). 63 residuals.uGARCHfilter-method (ARFIMAfit-class).uGARCHmultifit-method (uGARCHfit-class). 50 persistence. 63 (uGARCHmultifilter-class).ANY-method (ARFIMAfilter-class).ANY-method (multiforecast-methods). 22 nyblom.uGARCHmultifilter-method persistence (uGARCHfit-class).uGARCHmultispec-method (multifit-methods). 71–74.missing-method (uGARCHfit-class). 71 persistence. 71 persistence. 54 plot.uGARCHboot. 29. 7.ARFIMAroll-method (ARFIMAroll-class).missing.ARFIMAfit-method newsimpact. 22–24. 63 residuals. 26.missing-method (uGARCHfilter-class). 47 multiforecast. 50 .numeric. 48 multiforecast-methods. 47 multifit. 63 pdist (rgarchdist).missing. 50 rdist (rgarchdist).missing-method (uGARCHdistribution-class). 4 multiforecast (multiforecast-methods). 13 (uGARCHfilter-class). 60 rGARCH-class. 76.missing.missing. 4.ARFIMAfilter-method newsimpact. 63 residuals. 68 plot.missing.ANY-method (uGARCHroll-class).missing. 49 INDEX persistence. 49 multispec.ARFIMAmultispec-method (multifit-methods). 80.uGARCHdistribution. 31.ANY.ARFIMAmultispec-method (multiforecast-methods). 76 newsimpact (uGARCHfit-class). 48 multispec.missing.uGARCHmultispec-method (multiforecast-methods). 4 multispec (multispec-methods). 50 report (uGARCHroll-class).missing-method (uGARCHroll-class). 57.uGARCHfilter. 10 (uGARCHfit-class). 48 multiforecast.92 multifit. 21 (uGARCHfit-class).uGARCHroll. 60 (uGARCHfit-class).ANY.ARFIMAmultifilter-method newsimpact.ANY-method (multispec-methods).ANY. 63 (ARFIMAmultifit-class). 63 plot.uGARCHfit-method (uGARCHfilter-class).missing-method (uGARCHsim-class).uGARCHforecast.uGARCHfilter-method nyblom.uGARCHroll-method (uGARCHroll-class). 60 residuals.ANY-method (uGARCHfit-class).missing-method (uGARCHfit-class).uGARCHfit-method (ARFIMAmultifilter-class). 63. (uGARCHfit-class).character. 80 qdist (rgarchdist). 63 sigma.vector-method (uGARCHspec-class). 71 signbias (uGARCHfit-class).ARFIMAfilter-method (ARFIMAfilter-class).ARFIMAspec. 75 setstart<. 10 show. 24 show. 83 setfixed<-. 54 . 13 show.uGARCHfilter-method (uGARCHfilter-class). 63 signbias-methods (uGARCHfit-class). 63 93 show. 21 show.uGARCHfilter-method (uGARCHfilter-class).uGARCHmultifilter-method (uGARCHmultifilter-class). 83 setstart<-.vector-method (uGARCHspec-class).ANY. 71 show. 83 sigma (uGARCHfit-class).ANY. 83 show. 23 show. 55 ugarchboot. 60 sigma.ARFIMApath-method (ARFIMApath-class).uGARCHpath-method (uGARCHpath-class).uGARCHmultispec-method (uGARCHmultispec-class).uGARCHspec-method (ugarchboot-methods). 57 show.ANY-method (ugarchboot-methods). 70.INDEX rugarch (rugarch-package). 73 show. 79. 74 show. 63 signbias. 80 show. 3 rugarch-package.uGARCHforecast-method (uGARCHforecast-class).ARFIMAspec-method (ARFIMAspec-class). 53 uGARCHboot.uGARCHfit-method (ugarchboot-methods). 76 show.vector-method (ARFIMAspec-class).ANY-method (uGARCHfit-class).uGARCHspec. 29 show.ARFIMAdistribution-method (ARFIMAdistribution-class).uGARCHboot-method (uGARCHboot-class). 63 sp5 ret. 83 setfixed<-.(uGARCHspec-class). 71 sigma.uGARCHmultifit-method (uGARCHmultifit-class).uGARCHmultifit-method (uGARCHmultifit-class). 62.ARFIMAmultispec-method (ARFIMAmultispec-class).ARFIMAfit-method (ARFIMAfit-class). 71 show. 23 show. 30 show.vector-method (ARFIMAspec-class). 52 ugarchbench.ANY-method (uGARCHspec-class). 5.(uGARCHspec-class).ARFIMAmultiforecast-method (ARFIMAmultiforecast-class). 72 show.uGARCHdistribution-method (uGARCHdistribution-class).uGARCHfilter-method (uGARCHfilter-class). 83 setfixed<-.ARFIMAspec.uGARCHspec.ARFIMAforecast-method (ARFIMAforecast-class). 82 ugarchboot (ugarchboot-methods).uGARCHroll-method (uGARCHroll-class). 63 sigma. 3 setfixed<.ARFIMAmultifit-method (ARFIMAmultifit-class).uGARCHfit-method (uGARCHfit-class). 30 setfixed<-. 55 ugarchboot. 22 show. 4.uGARCHfit-method (uGARCHfit-class). 83 setstart<-. 67. 76.uGARCHspec-method (uGARCHspec-class). 7 show. 54 show.uGARCHfit-method (uGARCHfit-class).ARFIMAmultifilter-method (ARFIMAmultifilter-class). 56 ugarchboot. 60.ANY-method (uGARCHspec-class). 63 signbias.uGARCHsim-method (uGARCHsim-class). 60 show.ANY-method (uGARCHfit-class). 55 ugarchboot.ARFIMAsim-method (ARFIMAsim-class). 63 sigma. 17 show. 55 uGARCHboot-class. 68 show.uGARCHmultifilter-method (uGARCHmultifilter-class).uGARCHmultiforecast-method (uGARCHmultiforecast-class). 60 signbias. 30 setstart<-. 58 uGARCHfilter. 75. 76. 73 uGARCHmultifilter-class. 60. 63 uncmean. 55. 74.ANY-method (uGARCHfit-class). 58 ugarchdistribution.uGARCHspec-method (ugarchpath-methods). 4. 65. 76. 56. 76 ugarchpath. 61 uGARCHfilter-class. 4. 73 uGARCHpath. 76. 79. 54. 67. 81 uGARCHspec. 46–49. 70. 63 uncmean. 47.uGARCHspec-method (ugarchforecast-methods). 71. 60. 79 ugarchroll. 80. 69 uGARCHforecast-class. 64. 80.ANY-method (ugarchdistribution-methods). 67. 56. 82 ugarchroll (ugarchroll-methods). 4. 54. 70. 76. 71–73 uGARCHmultiforecast-class. 74 ugarchpath-methods. 4. 69 ugarchforecast. 54. 61 ugarchfilter.ANY-method (ugarchforecast-methods). 62. 69 ugarchforecast. 76. 69. 83.ANY-method (ugarchfit-methods).ANY-method (ugarchspec-methods).uGARCHspec-method (ugarchfit-methods). 75 uGARCHpath-class. 73 uGARCHmultifit-class. 61 ugarchfilter. 78 uGARCHsim.ANY-method (ugarchroll-methods). 79. 78 ugarchroll.94 ugarchboot-methods. 56. 70. 84 uGARCHspec-class.uGARCHfit-method (ugarchsim-methods).uGARCHfit-method (ugarchforecast-methods). 46–48. 80. 82 ugarchspec (ugarchspec-methods). 75 ugarchpath. 82 ugarchdistribution (ugarchdistribution-methods). 62. 56. 66. 82 ugarchforecast (ugarchforecast-methods). 62. 67. 58. 86 ugarchspec. 56. 67. 49. 78 uGARCHroll-class. 55 uGARCHdistribution. 70. 83 ugarchfit. 46.uGARCHspec-method (ugarchroll-methods). 4. 69. 74. 71–73 uGARCHmultispec-class. 62. 81 uGARCHsim-class. 79. 58. 56. 83 ugarchspec-methods. 74. 4 ugarchpath (ugarchpath-methods). 84 ugarchspec.uGARCHfit-method (ugarchdistribution-methods). 82 ugarchfilter (ugarchfilter-methods). 69. 61 uGARCHfit. 63 ugarchfit-methods. 80 ugarchsim-methods. 76 ugarchroll-methods. 71 uGARCHmultifit. 81 ugarchsim.uGARCHspec-method (ugarchdistribution-methods). 66. 65. 81 ugarchsim. 60 ugarchfilter-methods. 69 ugarchforecast. 60. 71 uGARCHmultiforecast. 60–62 ugarchfilter. 55. 49. 67. 66 ugarchfit. 62. 82. 76. 79. 70. 75 ugarchpath. 58 uGARCHdistribution-class. 84 uncmean (uGARCHfit-class). 77. 56. 76. 75 uGARCHroll. 58 ugarchdistribution. 66 uGARCHfit-class. 74. 66 ugarchfit.uGARCHspec-method (ugarchfilter-methods).ANY-method (ugarchfilter-methods). 57 ugarchdistribution-methods. 82. 78 ugarchroll. 69 uGARCHmultifilter. 79. 66 uGARCHforecast. 85 ugarchfit (ugarchfit-methods). 67. 58. 65. 79 ugarchsim (ugarchsim-methods). 60. 72 uGARCHmultispec. 67. 72. 59 ugarchdistribution. 70. 62. 60.ANY-method (ugarchsim-methods). 62. 83 ugarchsim. 46. 58 ugarchdistribution. 61.ANY-method (ugarchpath-methods). 68 INDEX ugarchforecast-methods.ARFIMAfilter-method . 83 ugarchforecast. 60. 4. 81. missing.missing. 87 WeekDayDummy. 63 uncmean.ANY.missing. 63 uncvariance.character-method (WeekDayDummy-methods).numeric. 10 uncmean. 5 WeekDayDummy (WeekDayDummy-methods).missing. 83 vcov.missing.uGARCHfit-method (uGARCHfit-class).missing. 63 WeekDayDummy.INDEX (ARFIMAfilter-class).missing. 60 uncvariance.missing.character.uGARCHfilter.ARFIMAspec-method (ARFIMAspec-class). 60 uncmean.ANY-method (uGARCHfit-class). 63 uncvariance.uGARCHfit. 30 uncmean.ANY-method (uGARCHfit-class). 87 95 .ANY-method (WeekDayDummy-methods).ANY.ANY.character.ANY.ANY.missing.ANY.uGARCHspec-method (uGARCHspec-class).missing-method (uGARCHspec-class).missing. 63 uncvariance.missing-method (uGARCHfit-class).uGARCHfilter-method (uGARCHfilter-class).uGARCHspec. 87 WeekDayDummy.uGARCHfit-method (uGARCHfit-class).missing.ARFIMAfit-method (ARFIMAfit-class). 83 uncvariance (uGARCHfit-class). 63 uncvariance.missing-method (uGARCHfilter-class). 87 WeekDayDummy-methods.missing. 13 uncmean.missing.