Package 'rugarch'

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 of including external regressors. Finally, a set of feature rich distributions are used for modelling innovations and documented in the vignette.
This package is part of what used to be the rgarch package, which was split into univariate (rugarch) and multivariate (rmgarch) models for easier maintenance and use, both of which are now hosted on CRAN (stable) and bitbucket (development).

Details

While the package has implemented some safeguards, both during pre-estimation as well as the estimation phase, there is no guarantee of convergence in the fitting procedure. As a result, 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).
The functionality of the packages is contained in the main methods for defining a specification ugarchspec, fitting ugarchfit, forecasting ugarchforecast, simulation from fit object ugarchsim, path simulation from specification object ugarchpath, parameter distribution by simulation ugarchdistribution, bootstrap forecast ugarchboot and rolling estimation and forecast ugarchroll. There are also some functions which enable multiple fitting of assets in an easy to use wrapper with the option of multicore functionality, namely multispec, multifit, multifilter and multiforecast. Explanations on the available methods for the returned classes can be found in the documentation for those classes.
A separate subset of methods and classes has been included to calculate pure ARFIMA models with constant variance. This subset includes similar functionality as with the GARCH methods, with the exception that no plots are yet implemented, and neither is a forecast based on the bootstrap. These may be added in the future. While there are limited examples in the documentation on the ARFIMA methods, the interested user can search the rugarch.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, no representation is made about the adequacy of ARFIMA models, particularly the statistical properties of parameters when using distributions which go beyond the Gaussian.
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, distribution, quantile, sampling and fitting. Additionally, 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, to the standard ‘alpha-beta-delta-mu’ parametrization of the Generalized Hyperbolic Distribution family.
The type of data handled by the package is now completely based on the xts package, and only data which can be coerced to such will be accepted by the package. For the estimation and filter routines, some of the main extractors methods will now also return xts objects.
Some benchmarks (published and comparison with commercial package), are available through the ugarchbench function. The ‘inst’ folder of the source distribution also contains various tests which can be sourced and run by the user, also exposing some finer details of the functionality of the package. The user should really consult the examples supplied in this folder which are quite numerous and instructive with some comments.
Since version 1.0-14, all parallel estimation is carried out through a user-supplied cluster object, created from the parallel package, meaning that the user is now in control of managing the cluster lifecycle. This greatly simplifies the parallel estimation process and adds a layer of flexibility to the type of resources supported.
Finally, the global extractor functions sigma and fitted will now work with almost all returned classes and the return the conditional sigma and mean values, whether these are from an estimated, filtered, forecast, or simulated object (and their multi- function equivalents).

How to cite this package

Whenever using this package, please cite as

@Manual{Ghalanos_2014,
 author       = {Alexios Ghalanos},
 title        = {{rugarch}: Univariate GARCH models.},
 year         = {2014},
 note         = {R package version 1.4-0.},}

License

The releases of this package is licensed under GPL version 3.

Author(s)

Alexios Ghalanos

References

Baillie, R.T. and Bollerslev, T. and Mikkelsen,H.O. 1996, Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 3–30 .
Berkowitz, J. 2001, Testing density forecasts, with applications to risk management, Journal of Business and Economic Statistics, 19(4), 465–474.
Bollerslev, T. 1986, Generalized Autoregressive Conditional Heteroskedasticity 1986, Journal of Econometrics, 31, 307–327.
Ding, Z., Granger, C.W.J. and Engle, R.F. 1993, A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance, 1, 83–106.
Engle, R.F. and Ng, V. K. 1993, Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48, 1749–1778.
Engle, R. F., and Sokalska, M. E. 2012, Forecasting intraday volatility in the US equity market. Multiplicative component GARCH. Journal of Financial Econometrics, 10(1), 54–83.
Fisher, T. J., and Gallagher, C. M. 2012, New weighted portmanteau statistics for time series goodness of fit testing, Journal of the American Statistical Association, 107(498), 777–787.
Glosten, L.R., Jagannathan, R. and Runkle, D.E. 1993, On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance, 48(5), 1779–1801.
Hansen, B.E. 1990, Langrange Multiplier Tests for Parameter Instability in Non-Linear Models, mimeo.
Hentschel, Ludger. 1995, All in the family Nesting symmetric and asymmetric GARCH models, Journal of Financial Economics, 39(1), 71–104.
Nelson, D.B. 1991, Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370.
Pascual, L., Romo, J. and Ruiz, E. 2004, Bootstrap predictive inference for ARIMA processes, Journal of Time Series Analysis.
Pascual, L., Romo, J. and Ruiz, E. 2006, Bootstrap prediction for returns and volatilities in GARCH models, Computational Statistics and Data Analysis.
Vlaar, P.J.G. and Palm, F.C. 1993, The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion Conditional Heteroskedasticity and Jumps, Journal of Business and Economic Statistics, 11, 351–360.

Description

The virtual parent class of the ARFIMA subset.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "ARFIMA" in the signature.

Author(s)

Alexios Ghalanos

Description

Implements a cross validation method for ARFIMAX models

Usage

arfimacv(data, indexin, indexout, ar.max = 2, ma.max = 2, 
criterion = c("rmse","mae","berkowitzp"),berkowitz.significance = 0.05, 
arfima = FALSE, include.mean = NULL, distribution.model = "norm",
cluster = NULL, external.regressors = NULL, solver = "solnp", 
solver.control=list(), fit.control=list(), return.best=TRUE)

Arguments

Details

The function evaluates all possible combinations of the ARFIMAX model for all the training and testing sets supplied. For the ARMA orders, the orders are evaluated fully (e.g. for ar.max=2, all possible combinations are evaluated including AR(0,0), AR(0,1), AR(0,2), AR(1,0), AR(2,0) AR(1,2), AR(2,1), and AR(2,2)). For each training set in indexin, all model combinations are evaluated and the 1-ahead rolling forecast for the indexout testing set is produced and compared to the realized values under the 3 criteria listed. Once all training/testing is done on all model combinations, the criteria are averaged across all the sets for each combination and the results returned.

Value

A list with the following items:

Note

Use a cluster...this is an expensive computation, particularly for large ar.max and ma.max orders. The indexin and indexout lists are left to the user to decide how to implement.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
require(xts)
require(parallel)
data(sp500ret)
spx = as.xts(sp500ret)
nn = nrow(spx)
nx = nn-round(0.9*nn,0)
if(nx
h = (nx/50)-1
indexin = lapply(1:h, function(j){ tail(seq(1,(nn-nx)+j*50, by=1),250) })
indexout = lapply(indexin, function(x){ (tail(x,1)+1):(tail(x,1)+50) })
cl = makePSOCKcluster(5)
mod = arfimacv(spx, indexin, indexout, ar.max = 2, ma.max = 2, 
criterion = c("rmse","mae","berkowitzp")[1],
berkowitz.significance = 0.05, arfima = FALSE, include.mean = NULL, 
distribution.model = "norm", cluster = cl, external.regressors = NULL, 
solver = "solnp")
stopCluster(cl)

## End(Not run)

Description

Class for the ARFIMA Parameter Distribution, objects of which are created by calling function arfimadistribution.

Slots

dist:

Object of class "vector" Details of fitted parameters.

truecoef:

Object of class "matrix" The actual coefficients.

model:

Object of class "list" The model specification.

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

as.data.frame

signature(x = "ARFIMAdistribution"): extracts various values from object (see note).

show

signature(object = "ARFIMAdistribution"): parameter distribution summary.

Note

The as.data.frame function takes optionally 2 additional arguments, namely window which indicates the particular distribution window number for which data is required (is usually just 1 unless the recursive option was used), and which indicating the type of data required. Valid values for the latter are “rmse” for the root mean squared error between simulation fit and actual parameters, “stats” for various statistics computed for the simulations such as log likelihood, persistence, unconditional variance and mean, “coef” for the estimated coefficients (i.e. the parameter distribution and is the default choice), and “coefse” for the estimated robust standard errors of the coefficients (i.e. the parameter standard error distribution).

Author(s)

Alexios Ghalanos

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.

Usage

arfimadistribution(fitORspec, n.sim = 2000, n.start = 1, m.sim = 100, 
recursive = FALSE, recursive.length = 6000, recursive.window = 1000, 
prereturns = NA, preresiduals = NA, rseed = NA, 
custom.dist = list(name = NA,  distfit = NA, type = "z"), mexsimdata = NULL, 
fit.control = list(), solver = "solnp", solver.control = list(), 
cluster = NULL, ...)

Arguments

Details

This method facilitates the simulation and evaluation of the uncertainty of ARFIMA model parameters. The recursive option also allows the evaluation of the simulation based consistency (in terms of sqrt(N) ) of the parameters as the length (n.sim) of the data increases, in the sense of the root mean square error (rmse) of the difference between the simulated and true (hypothesized) parameters.
This is an expensive function, particularly if using the recursive option, both on memory and CPU resources, performing many re-fits of the simulated data in order to generate the parameter distribution.

Value

A ARFIMAdistribution object containing details of the ARFIMA simulated parameters distribution.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA filter.

Slots

filter:

Object of class "vector"

model:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

coef

signature(object = "ARFIMAfilter"): Extracts the coefficients.

fitted

signature(object = "ARFIMAfilter"): Extracts the filtered values.

infocriteria

signature(object = "ARFIMAfilter"): Calculates and returns various information criteria.

likelihood

signature(object = "ARFIMAfilter"): Extracts the likelihood.

residuals

signature(object = "ARFIMAfilter"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

show

signature(object = "ARFIMAfilter"): Filter summary.

uncmean

signature(object = "ARFIMAfilter"): Calculates and returns the unconditional mean. Takes additional arguments ‘method’ with option for “analytical” or “simulation”, ‘n.sim’ for the number of simulations (if that method was chosen, and defaults to 100000) and ‘rseed’ for the simulation random generator initialization seed. Note that the simulation method is only available for a fitted object or specification with fixed parameters, and not for the filtered object.

Author(s)

Alexios Ghalanos

Examples

showClass("ARFIMAfilter")

Description

Method for filtering an ARFIMA model.

Usage

arfimafilter(spec, data, out.sample = 0, n.old=NULL, ...)

Arguments

Details

The n.old argument is optional and indicates the length of the original data (in cases when this represents a dataseries augmented by newer data). 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. 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.

Value

A ARFIMAfilter object containing details of the ARFIMA filter.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA fit.

Slots

fit:

Object of class "vector"

model:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

coef

signature(object = "ARFIMAfit"): Extracts the coefficients.

fitted

signature(object = "ARFIMAfit"): Extracts the fitted values.

infocriteria

signature(object = "ARFIMAfit"): Calculates and returns various information criteria.

likelihood

signature(object = "ARFIMAfit"): Extracts the likelihood.

residuals

signature(object = "ARFIMAfit"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

show

signature(object = "ARFIMAfit"): Fit summary.

uncmean

signature(object = "ARFIMAfit"): Calculates and returns the unconditional mean. Takes additional arguments ‘method’ with option for “analytical” or “simulation”, ‘n.sim’ for the number of simulations (if that method was chosen, and defaults to 100000) and ‘rseed’ for the simulation random generator initialization seed.

vcov

signature(object = "ARFIMAfit"): Extracts the covariance matrix of the parameters. Additional logical option of ‘robust’ indicates whether to extract the robust based covariance matrix.

convergence

signature(object = "ARFIMAfit"): Returns the solver convergence code for the fitted object (zero denotes convergence).

reduce

signature(object = "ARFIMAfit"): Zeros parameters (fixing to zero in rugarch is equivalent to eliminating them in estimation) with p-values (optional argument “pvalue”) greater than 0.1 (default), and re-estimates the model. Additional arguments are passed to arfimafit.An additional option “use.robust” (default TRUE) asks whether to use the robust calculated p-values.

getspec

signature(object = "ARFIMAfit"): Extracts and returns the ARFIMA specification from a fitted object.

Author(s)

Alexios Ghalanos

Examples

showClass("ARFIMAfit")

Description

Method for fitting an ARFIMA models.

Usage

arfimafit(spec, data, out.sample = 0, solver = "solnp", solver.control = list(), 
fit.control = list(fixed.se = 0, scale = 0), numderiv.control = list(grad.eps=1e-4, 
grad.d=0.0001, grad.zero.tol=sqrt(.Machine$double.eps/7e-7), hess.eps=1e-4, hess.d=0.1, 
hess.zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2), ...)

Arguments

Details

The ARFIMA optimization routine first calculates a set of feasible starting points which are used to initiate the ARFIMA Maximum Likelihood recursion. The main part of the likelihood calculation is performed in C-code for speed.
The out.sample option is provided in order to carry out forecast performance testing against actual data. A minimum of 5 data points are required for these tests. If the out.sample option is positive, then the routine will fit only N - out.sample (where N is the total data length) data points, leaving out.sample points for forecasting and testing using the forecast performance measures. In the arfimaforecast routine the n.ahead may also be greater than the out.sample number resulting in a combination of out of sample data points matched against actual data and some without, which the forecast performance tests will ignore.
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). The solver.control list then accepts the following additional (to the solnp) arguments: “n.restarts” is the number of solver restarts required (defaults to 1), “parallel” (logical), “pkg” (either snowfall or multicore) and “cores” (the number of cores or workers to use) for use of parallel functionality, “rseed” is the seed to initialize the random number generator, and “n.sim” is the number of simulated parameter vectors to generate per n.restarts.

Value

A ARFIMAfit object containing details of the ARFIMA fit.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA forecast.

Slots

forecast:

Object of class "vector"

model:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

fitted

signature(x = "ARFIMAforecast"): The n.ahead by n.roll+1 matrix of conditional mean forecasts. The column names are the T[0] dates.

fpm

signature(object = "ARFIMAforecast"): Forecast performance measures.

show

signature(object = "ARFIMAforecast"): Forecast summary returning the 0-roll frame only.

Note

Since versions 1.01-3, the fitted method has been introduced which extracts the n.ahead by (n.roll+1) matrix of conditional mean forecasts, with column names the T[0] time index. This is unlike the old data.frame which returned the T+1 etc dates. This method is the default extractor in rugarch package for the conditional mean (whether from an estimated, filtered, forecast or simulated object) and the other method, namely as.data.frame is now deprecated with the exception of a few classes where it is still used (ARFIMAdistribution and ARFIMAroll).
The fpm method returns the Mean Squared Error (MSE), Mean Absolute Error (MAE), Directional Accuracy (DAC) and number of points used for the calculation (N), of forecast versus realized returns, if the extra summary option is set to TRUE (default). This is a 4 x (n.roll+1) matrix, with row headings the T[0] time index, and requires at least 5 points to calculate the summary measures else will return NA. When n.ahead>1, this method calculates the measures on the n.ahead>1 unconditional forecast, but if n.ahead=1 with n.roll>4, it will calculate the measures on the rolling forecast instead. Finally, when summary is set to FALSE, the method will return a list of length n.roll+1 of xts objects with the loss functions (Squared Error and Absolute Error and Directional Hits).

Author(s)

Alexios Ghalanos

Description

Method for forecasting from an ARFIMA model.

Usage

arfimaforecast(fitORspec, data = NULL, n.ahead = 10, n.roll = 0, out.sample = 0, 
external.forecasts = list(mregfor = NULL), ...)

Arguments

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 a specification object (in which case the data is required) with the parameters entered via the set.fixed<- methods on an ARFIMAspec object.
One step ahead forecasts are based on the value of the previous data, while n-step ahead (n>1) are based on the unconditional mean of the model.
The ability to roll the forecast 1 step at a time is implemented with the n.roll argument which controls how many times to roll the n.ahead forecast. The default argument of n.roll = 0 denotes no rolling beyond the first forecast and returns the standard n.ahead forecast. Critically, since n.roll depends on data being available from which to base the rolling forecast, the arfimafit function needs to be called with the argument out.sample being at least as large as the n.roll argument, or in the case of a specification being used instead of a fit object, the out.sample argument directly in the forecast function.

Value

A ARFIMAforecast object containing details of the ARFIMA forecast. See the class for details on the returned object and methods for accessing it and performing some tests.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA Multiple filter.

Slots

filter:

Object of class "vector"

desc:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

fitted

signature(object = "ARFIMAmultifilter"): Extracts the fitted values.

residuals

signature(object = "ARFIMAmultifilter"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

coef

signature(object = "ARFIMAmultifilter"): Extracts the coefficients.

likelihood

signature(object = "ARFIMAmultifilter"): Extracts the likelihood.

show

signature(object = "ARFIMAmultifilter"): Filter summary.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA Multiple fit.

Slots

fit:

Object of class "vector"

desc:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

coef

signature(object = "ARFIMAmultifit"): Extracts the coefficients.

likelihood

signature(object = "ARFIMAmultifit"): Extracts the likelihood.

fitted

signature(object = "ARFIMAmultifit"): Extracts the fitted values.

residuals

signature(object = "ARFIMAmultifit"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

show

signature(object = "ARFIMAmultifit"): Fit summary.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA Multiple forecast.

Slots

forecast:

Object of class "vector"

desc:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

fitted

signature(x = "ARFIMAmultiforecast"): Extracts the conditional mean forecast from the object, and returns an array of the n.ahead by (n.roll+1) by n.assets.

show

signature(object = "ARFIMAmultiforecast"): forecast summary.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA Multiple specification.

Slots

spec:

Object of class "vector"

type:

Object of class "character"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

show

signature(object = "ARFIMAmultispec"): specification summary.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA Path simulation.

Slots

path:

Object of class "vector"

model:

Object of class "vector"

seed:

Object of class "integer"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

fitted

signature(x = "ARFIMApath"): Extracts the simulated path values as a matrix of dimension n.sim by m.sim.

show

signature(object = "ARFIMApath"): path simulation summary.

Author(s)

Alexios Ghalanos

Description

Method for simulating the path of an ARFIMA model. This is a convenience function which does not require a fitted object (see note below).

Usage

arfimapath(spec, n.sim = 1000, n.start = 0, m.sim = 1, prereturns = NA, 
	preresiduals = NA, rseed = NA, 
	custom.dist=list(name = NA, distfit = NA, type = "z"), mexsimdata=NULL, ...)

Arguments

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. Instead, an arfima spec object is required with the model parameters supplied via the setfixed<- argument to the spec.

Value

A ARFIMApath object containing details of the ARFIMA path simulation.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA rolling forecast.

Slots

forecast:

Object of class "vector"

model:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

as.data.frame

signature(x = "ARFIMAroll"): extracts various values from object (see note).

resume

signature(object = "ARFIMAroll"): Resumes a rolling backtest which has non-converged windows using alternative solver and control parameters.

fpm

signature(object = "ARFIMAroll"): Forecast performance measures.

coef

signature(object = "ARFIMAroll"): Extracts the list of coefficients for each estimated window in the rolling backtest.

report

signature(object = "ARFIMAroll"): roll backtest reports (see note).

show

signature(object = "ARFIMAroll"): Summary.

Note

The as.data.frame extractor method allows the extraction of either the conditional forecast density or the VaR. It takes additional argument which with valid values either “density” or “VaR”.
The coef method will return a list of the coefficients and their robust standard errors (assuming the keep.coef argument was set to TRUE in the ugarchroll function), and the ending date of each estimation window.
The report method takes the following additional arguments:
1.type for the report type. Valid values are “VaR” for the VaR report based on the unconditional and conditional coverage tests for exceedances (discussed below) and “fpm” for forecast performance measures.
2.VaR.alpha (for the VaR backtest report) is the tail probability and defaults to 0.01.
3.conf.level the confidence level upon which the conditional coverage hypothesis test will be based 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 method (separately from report) takes additional logical argument summary, which when TRUE will return the mean squared error (MSE), mean absolute error (MAE) and directional accuracy of the forecast versus realized returns. When FALSE, it will return a data.frame of the time series of squared (SE) errors, absolute errors (AE), directional hits (HITS), and a VaR Loss function described in Gonzalez-Rivera, Lee, and Mishra (2004) for each coverage level where it was calculated. This can then be compared, with the VaR loss of competing models using such tests as the model confidence set (MCS) of Hansen, Lunde and Nason (2011).

Author(s)

Alexios Ghalanos

Description

Method for creating rolling density forecast from ARFIMA models with option for refitting every n periods with parallel functionality.

Usage

arfimaroll(spec, data, n.ahead = 1, forecast.length = 500, 
n.start = NULL, refit.every = 25, refit.window = c("recursive", "moving"), 
window.size = NULL, solver = "hybrid", fit.control = list(), 
solver.control = list(), calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.05), 
cluster = NULL, keep.coef = TRUE, ...)

Arguments

Details

This is a wrapper function for creating rolling forecasts of the conditional ARFIMA density, and optionally calculating the Value at Risk at specified levels. The argument refit.every determines every how many periods the model is re-estimated. Given a dataset of length N, it is possible to choose either how many periods from the end to use for out of sample forecasting (using the forecast.length option), or the starting point for initializing the rolling forecast (and using all the data after that for the out of sample forecast). Only rolling 1-ahead forecasts are supported spanning the dataset, which should be useful for backtesting models. Anything more complicated should be wrapped by the user by making use of the underlying functions in the package. The function has 2 main methods for viewing the data, a standard plot method and a report methods (see class ARFIMAroll for details on how to use these methods). In case of no-convergence in some of all the windows, a new method called resume now allows to pass the returned (non-converged) object with new solver and control parameters to be re-estimated (only the non-converged windows are re-estimated). Parallel functionality is now based entirely on the parallel package, and it is up to the user to pass a cluster object, and then stop it once the routine is completed.

Value

An object of class ARFIMAroll.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
data(sp500ret)
spec = arfimaspec(distribution.model = "std")
mod = arfimaroll(spec, data = sp500ret, n.ahead = 1, 
n.start = 1000,  refit.every = 100, refit.window = "moving", 
solver = "hybrid", fit.control = list(),
calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05),
keep.coef = TRUE)
report(sp500.bktest, type="VaR", VaR.alpha = 0.01, conf.level = 0.95) 
report(sp500.bktest, type="fpm")

## End(Not run)

Description

Class for the ARFIMA simulation.

Slots

simulation:

Object of class "vector"

model:

Object of class "vector"

seed:

Object of class "integer"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

fitted

signature(x = "ARFIMAsim"): extracts the simulated values as a matrix of dimension n.sim by m.sim.

show

signature(object = "ARFIMAsim"): simulation summary.

Author(s)

Alexios Ghalanos

Description

Method for simulation from ARFIMA models.

Usage

arfimasim(fit, n.sim = 1000, n.start = 0, m.sim = 1, startMethod = 
	c("unconditional", "sample"), prereturns = NA, preresiduals = NA, 
	rseed = NA, custom.dist = list(name = NA, distfit = NA, type = "z"), 
	mexsimdata = NULL, ...)

Arguments

Details

The custom.dist option allows for defining a custom density which exists in the users workspace with methods for “r” (sampling, e.g. rnorm) and “d” (density e.g. dnorm). It must take a single fit object as its second argument. Alternatively, custom.dist can take any name in the name slot (e.g.“sample”) and a matrix in the fit slot with dimensions equal to m.sim (columns) and n.sim (rows).

Value

A ARFIMAsim object containing details of the ARFIMA simulation.

Author(s)

Alexios Ghalanos

Description

Class for the ARFIMA specification.

Slots

model:

Object of class "vector"

Extends

Class "ARFIMA", directly. Class "rGARCH", by class "ARFIMA", distance 2.

Methods

show

signature(object = "ARFIMAspec"): Specification summary.

setfixed<-

signature(object = "ARFIMAspec", value = "vector"): Sets the fixed parameters (which must be supplied as a named list).

setstart<-

signature(object = "ARFIMAspec", value = "vector"): Sets the starting parameters (which must be supplied as a named list).

setbounds<-

signature(object = "ARFIMAspec", value = "vector"): Sets the parameters lower and upper bounds, which must be supplied as a named list with each parameter being a numeric vector of length 2 i.e. "ar1"=c(-1,1)). If the vector is of length 1, then this is assumed to be the lower bound, and the upper bound will be set to its default value prior to estimation.

uncmean

signature(object = "ARFIMAspec"): Returns the unconditional mean of a specification which has been assigned fixed parameters.

Author(s)

Alexios Ghalanos

Description

Method for creating an ARFIMA specification object prior to fitting.

Usage

arfimaspec(mean.model = list(armaOrder = c(1, 1), include.mean = TRUE, 
    arfima = FALSE, external.regressors = NULL), distribution.model = "norm", 
    start.pars = list(), fixed.pars = list(), ...)

Arguments

Details

The specification allows for flexibility in ARFIMA modelling.
In order to understand which parameters can be entered in the start.pars and fixed.pars optional arguments, 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. Just increment the number for higher orders):
Mean Model:

Distribution Model:

Value

A ARFIMAspec object containing details of the ARFIMA specification.

Author(s)

Alexios Ghalanos

Description

Select best fitting ARFIMA models based on information criteria.

Usage

autoarfima(data, ar.max = 2, ma.max = 2, criterion = c("AIC","BIC","SIC","HQIC"),
method = c("partial", "full"), arfima = FALSE, include.mean = NULL, 
distribution.model = "norm", cluster = NULL, external.regressors = NULL, 
solver = "solnp", solver.control=list(), fit.control=list(), return.all = FALSE)

Arguments

Value

A list with the following items:

Author(s)

Alexios Ghalanos

Examples

## Not run: 
data(sp500ret)
fit = autoarfima(data = sp500ret[1:1000,], ar.max = 2, ma.max = 2, 
criterion = "AIC", method = "full")

## End(Not run)

Description

Implements the Berkowitz Density Forecast Likelihood Ratio Test.

Usage

BerkowitzTest(data, lags = 1, significance = 0.05, tail.test = FALSE, alpha = 0.05)

Arguments

Details

See not below.

Value

A list with the following items:

Note

The data must first be transformed before being submitted to the function as described here. Given a forecast density (d*) at time t, transform the actual(observed) realizations of the data by applying the distribution function of the forecast density (p*). This will result in a set of uniform values (see Rosenblatt (1952)). Transform those value into standard normal variates by applying the standard normal quantile function (qnorm). The example below hopefully clarifies this. 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). When tail.test is used, the test of the tail at the “alpha” quantile level is performed using a censored normal likelihood.

Author(s)

Alexios Ghalanos

References

Berkowitz, J. 2001, Testing density forecasts, with applications to risk management, Journal of Business and Economic Statistics, 19(4), 465–474.
Dowd, K. 2004, A modified Berkowitz back-test, RISK Magazine, 17(4), 86–87.
Jarque, C.M. and Bera, A.K. 1987, A test for normality of observations and regression residuals, International Statistical Review, 55(2), 163–172.
Rosenblatt, M. 1952, Remarks on a multivariate transformation, The Annals of Mathematical Statistics, 23(3), 470–472.

Examples

## Not run: 
#  A univariate GARCH model is used with rolling out of sample forecasts.
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(6,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "nig")
fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE], out.sample = 1000)
pred = ugarchforecast(fit, n.ahead = 1, n.roll = 999)
dmatrix = cbind(as.numeric(fitted(pred)),as.numeric(sigma(pred)), 
rep(coef(fit)["skew"],1000), rep(coef(fit)["shape"],1000))
colnames(dmatrix) = c("mu", "sigma", "skew", "shape")
# Get Realized (Oberved) Data
obsx = tail(dji30ret[,1], 1000)
# Transform to Uniform
uvector = apply(cbind(obsx,dmatrix), 1, FUN = function(x) pdist("nig", q = x[1],
mu = x[2], sigma = x[3], skew = x[4], shape = x[5]))

# hist(uvector)
# transform to N(0,1)
nvector = qnorm(uvector)
test1 = BerkowitzTest(data = nvector, lags = 1, significance = 0.05)
test2 = BerkowitzTest(data = nvector, alpha = 0.05, significance = 0.05, 
tail.test=TRUE)
test3 = BerkowitzTest(data = nvector, alpha = 0.01, significance = 0.05, 
tail.test=TRUE)

## End(Not run)

Description

Implements the Directional Accuracy Test of Pesaran and Timmerman and Excess Profitability Test of Anatolyev and Gerko.

Usage

DACTest(forecast, actual, test = c("PT", "AG"), conf.level = 0.95)

Arguments

Details

See the references for details on the tests. The Null is effectively that of independence, and distributed as N(0,1).

Value

A list with the following items:

Author(s)

Alexios Ghalanos

References

Anatolyev, S. and Gerko, A. 2005, A trading approach to testing for predictability, Journal of Business and Economic Statistics, 23(4), 455–461.
Pesaran, M.H. and Timmermann, A. 1992, A simple nonparametric test of predictive performance, Journal of Business and Economic Statistics, 10(4), 461–465.

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(6,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "nig")
fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE], out.sample = 1000)
pred = ugarchforecast(fit, n.ahead = 1, n.roll = 999)
# Get Realized (Oberved) Data
obsx = tail(dji30ret[,1], 1000)
forc = as.numeric(as.data.frame(pred,rollframe="all",align=FALSE,which="series"))
print(DACTest(forc, obsx, test = "PT", conf.level = 0.95))
print(DACTest(forc, obsx, test = "AG", conf.level = 0.95))

## End(Not run)

Description

These utilities will likely be useful for working with the forecast objects of the package which have a rather complex structure. In addition, the ftseq function is of particular value in generating intraday regularly spaced time and date sequences within a specific interval of times (e.g. 09:30 to 16:00).

Usage

move(index, by=1)
generatefwd(T0, length.out = 1, by = "days")
ftseq(T0, length.out, by, interval, exclude.weekends = TRUE)

Arguments

Details

Every object returned by one of the main methods in rugarch (including ugarchfit, ugarchfilter, ugarchforecast and ugarchsim) has a model slot attached which in turns hold details on the time index of the original dataset used (including a difftime object). In addition, extractors for the forecast class, uGARCHforecast, will usually return a matrix with the (n.roll+1) columns having the T+0 dates, and the rows names represented as characters ‘T+1,...,T+n’ indicating the forecast periods following the T+0 date.
For the rolling forecast, it is a simple matter to shift the T+0 date by 1 to obtain the actual forecast date. Because rolling forecasts are made using the ‘out.sample’ switch, this means that there is always an actual date attached to this forecast based on the realized out.sample data (with the exception of the case when n.roll=out.sample in which case the last forecast is completely out of the range of the dataset). One quick way of obtaining the actual T+1 rolling dates is to just pass the vector of T+0 dates to the move function as shown in the examples.
For the n.ahead>1 unconditional forecasts, there may or may not be actual dates in the dataset covering the period, depending on whether out.sample was used, n.roll was also used, and how these all come together to form a complex object of moving and unconditional forecasts (making this the most complex of forecast cases). One way to quickly generate a sequence of dates is to use the generatefwd function with the T+0 starting date, the ‘length’ as the n.ahead horizon and the ‘by’ the difftime object from the model slot, as shown in the examples.
Note that for both the move and generatefwd functions, weekends are excluded in order to try to return a more realistic value.
Finally, when working with Date/Time objects remember to set your time zone with Sys.setenv(TZ=).

Value

A vector of Date/Time/Numeric indices of the same class as used in the input.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
data(sp500ret)
spec = ugarchspec()
fit = ugarchfit(spec, sp500ret, out.sample=10)
forc = ugarchforecast(fit, n.ahead = 25, n.roll = 10)
f = fitted(forc)
# this is a 25 x 11 matrix [n.ahead x (n.roll+1)]
# colnames: T+0 date index
T0 = as.POSIXct(colnames(f))
rollT1 = move(T0, by=1)
# rolling estimation
plot(xts(f["T+1",],rollT1))
# unconditional estimates:
par(mfrow=c(3,4))
for(i in 1:11){
# difftime is always in model$modeldata$period
D=generatefwd(T0[i], length.out = 25, by = forc@model$modeldata$period)
plot(xts(f[,i], D), main=paste("T+0:",as.character(T0[i]),sep=""), auto.grid=FALSE)
}
############################
## Intraday Sequency Example
############################
T0 = as.POSIXct("2001-01-01 16:00:00")
# remember to remove the backslash from the code below
interval = format(seq(as.POSIXct("2001-01-01 09:30:00"), as.POSIXct("2001-01-01 16:00:00"), 
by="min"), "%H:%M:%S")
by = "mins"
length.out=1000
R = ftseq(T0, length.out, by, interval)

## End(Not run)

Description

Dow Jones 30 Constituents closing value log returns from 1987-03-16 to 2009-02-03 from Yahoo Finance. Note that AIG was replaced by KFT (Kraft Foods) on September 22, 2008. This is not reflected in this data set as that would bring the starting date of the data to 2001.

Usage

data(dji30ret)

Format

A data.frame containing 30x5521 observations.

Source

Yahoo Finance

Description

The Bollerslev-Ghysel benchmark dataset. The variables in the data set are:
1. The daily percentage nominal returns computed as 100 [ln(Pt) - ln(Pt-1)], where Pt is the bilateral Deutschemark/British pound rate constructed from the corresponding U.S. dollar rates.
2. A dummy variable that takes the value of 1 on Mondays and other days following no trading in the Deutschemark or British pound/ U.S. dollar market during regular European trading hours and 0 otherwise.

Usage

data(dmbp)

Format

A data.frame containing 2x1974 observations.

References

Bollerslev, T. and Ghysels, E. 1996, Periodic Autoregressive Conditional Heteroscedasticity , Journal of Business and Economic Statistics, 14, 139–151.

Description

Implements the Expected Shortfall Test of McNeil and Frey.

Usage

ESTest(alpha = 0.05, actual, ES, VaR, conf.level = 0.95, 
boot = FALSE, n.boot = 1000)

Arguments

Details

The Null hypothesis is that the excess conditional shortfall (excess of the actual series when VaR is violated), is i.i.d. and has zero mean. The test is a one sided t-test against the alternative that the excess shortfall has mean greater than zero and thus that the conditional shortfall is systematically underestimated. Using the bootstrap to obtain the p-value should alleviate any bias with respect to assumptions about the underlying distribution of the excess shortfall.

Value

A list with the following items:

Author(s)

Alexios Ghalanos

References

McNeil, A.J. and Frey, R. and Embrechts, P. (2000), Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance,7, 271–300.

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
fit = ugarchfit(spec, data = dji30ret[1:1000, 1, drop = FALSE])
spec2 = spec
setfixed(spec2)<-as.list(coef(fit))
filt = ugarchfilter(spec2, dji30ret[1001:2500, 1, drop = FALSE], n.old = 1000)
actual = dji30ret[1001:2500,1]
# location+scale invariance allows to use [mu + sigma*q(p,0,1,skew,shape)]
VaR = fitted(filt) + sigma(filt)*qdist("sstd", p=0.05, mu = 0, sigma = 1, 
skew  = coef(fit)["skew"], shape=coef(fit)["shape"])
# calculate ES
f = function(x) qdist("sstd", p=x, mu = 0, sigma = 1, 
skew  = coef(fit)["skew"], shape=coef(fit)["shape"])
ES = fitted(filt) + sigma(filt)*integrate(f, 0, 0.05)$value/0.05
print(ESTest(0.05, actual, ES, VaR, boot = TRUE))

## End(Not run)

Description

High Level GARCH bootstrap class to hold the univariate and multivariate boot objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHboot" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHboot")

Description

High Level GARCH parameter distribution class to hold the univariate and multivariate boot objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHdistribution" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHdistribution")

Description

High Level GARCH filter class to hold the univariate and multivariate filter objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHfilter" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHfilter")

Description

High Level GARCH fit class to hold the univariate and multivariate fits objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHfit" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHfit")

Description

High Level GARCH forecast class to hold the univariate and multivariate forecast objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHforecast" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHforecast")

Description

High Level GARCH Path simulation class to hold the univariate and multivariate path simulation objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHpath" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHpath")

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", directly.

Methods

No methods defined with class "GARCHroll" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHroll")

Description

High Level GARCH simulation class to hold the univariate and multivariate simulation objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHsim" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHsim")

Description

High Level GARCH spec class to hold the univariate and multivariate spec objects.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHspec" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHspec")

Description

GARCH High level inference and other tests class.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "rGARCH", directly.

Methods

No methods defined with class "GARCHtests" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("GARCHtests")

Description

The function scales the distributions from the (0, 1) zeta-rho GARCH parametrization to the alpha-beta parametrization and performs the appropriate scaling to the parameters given the estimated sigma and mu.

Usage

ghyptransform(mu = 0, sigma = 1,  skew = 0, shape = 3, lambda = -0.5)

Arguments

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.

References

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.

Description

Implements the GMM Orthogonality Test of Hansen.

Usage

GMMTest(z, lags = 1, skew=0, kurt=3, conf.level = 0.95)

Arguments

Details

This is a mispecification test based on Hansen's GMM procedure. Under a correctly specified model, certain population moment conditions should be satisfied and hold in the sample using the standardized residuals. The moment conditions can be tested both individually using a t-test or jointly using a Wald test (the vignette gives more details). The test returns a matrix (moment.mat) containing the first 4 moments statistics, their standard errors and t-values (2-sided t-test with alternative hypothesis that the value is not equal to zero). The matrix of joint conditions (joint.mat) contains the t-values and critical values of ‘Q2’, ‘Q3’ and ‘Q4’ representing the autocorrelation, given the chosen lags in the second, third and fourth moments and distributed as chi-squared with n.lag d.o.f, and the joint test (‘J’) for all moment conditions distributed chi-squared with 4+(n.lagx3) d.o.f.

Value

A list with the following items:

Author(s)

Alexios Ghalanos

References

Hansen, L. (1982), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50(4), 1029–1054.

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE])
z = residuals(fit)\/sigma(fit)
skew = dskewness("sstd",skew = coef(fit)["skew"], shape= coef(fit)["shape"])
# add back 3 since dkurtosis returns the excess kurtosis
kurt = 3+dkurtosis("sstd",skew = coef(fit)["skew"], shape= coef(fit)["shape"])
print(GMMTest(z, lags = 1, skew=skew, kurt=kurt))

## End(Not run)

Description

Implements the Non-Parametric Density Test of Hong and Li.

Usage

HLTest(PIT, lags = 4, kernel = "quartic", conf.level = 0.95)

Arguments

Details

A novel method to analyze how well a conditional density fits the underlying data is through the probability integral transformation (PIT) discussed in Rosenblatt (1952) and used in the BerkowitzTest. More recently, Hong and Li (2005) introduced a nonparametric portmanteau test, building on the work of Ait-Sahalia (1996), which tests the joint hypothesis of i.i.d and uniformity for a series of PIT transformed data. To achieve this, it tests for misspecification in the conditional moments of the model transformed standardized residuals, and is distributed as N(0, 1) under the Null of a correctly specified model. These moment tests are reported as ‘M(1,1)’ to ‘M(4,4)’ in the output, with ‘M(1,2)’ related to ARCH-in-mean effects, and ‘M(2,1)’ to leverage, while ‘W’ is the Portmanteu type test statistic for general misspecification (using p lags) and also distributed as N(0, 1) under the Null of a correctly specified model. Only upper tail critical values are used in this test. The interested reader is referred to the paper for more details.

Value

A list with the following items:

Author(s)

Alexios Ghalanos

References

Ait-Sahalia, Y. (1996), Testing continuous-time models of the spot interest rate, Review of Financial Studies, 9(2), 385–426.
Berkowitz, J. (2001), Testing density forecasts, with applications to risk management, Journal of Business and Economic Statistics, 19(4), 465–474.
Hong, Y., and Li, H. (2005), Nonparametric specification testing for continuous-time models with applications to term structure of interest rates, Review of Financial Studies, 18(1), 37–84.
Rosenblatt, M. (1952), Remarks on a multivariate transformation, The Annals of Mathematical Statistics, 23(3), 470–472.

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
fit = ugarchfit(spec, data = dji30ret[, 1, drop = FALSE])
z = residuals(fit)/sigma(fit)
PIT = pdist("sstd",z, mu = 0, sigma = 1, skew = coef(fit)["skew"], 
shape=coef(fit)["shape"])
print(HLTest(PIT, lags=4))

## End(Not run)

Description

Implements the Model Confidence Set Test procedure of Hansen, Lunde and

Usage

mcsTest(losses, alpha, nboot = 100, nblock = 1, boot = c("stationary", "block"))

Arguments

Details

Calculates and returns the results of both the R (range) and SQ (semi-quadratic) statistics.

Value

A list with the following items:

Author(s)

Alexios Ghalanos

References

Hansen, P. R., Lunde, A., and Nason, J. M., 2011. The model confidence set. Econometrica, 79(2), 453–497.

Description

Method for multiple filtering of a variety of univariate GARCH and ARFIMA models.

Usage

multifilter(multifitORspec, data = NULL, out.sample = 0, n.old = NULL, 
rec.init = "all", cluster = NULL, ...)

Arguments

Value

A uGARCHmultifilter object containing details of the multiple GARCH filter. A ARFIMAmultifilter object containing details of the multiple ARFIMA filter.

Author(s)

Alexios Ghalanos

Description

Method for multiple fitting a variety of univariate GARCH and ARFIMA models.

Usage

multifit(multispec, data, out.sample = 0, solver = "solnp", solver.control = list(), 
fit.control = list(stationarity = 1, fixed.se = 0, scale = 0, rec.init = "all"), 
cluster = NULL, ...)

Arguments

Value

A uGARCHmultifit or ARFIMAmultifit object containing details of the GARCH or ARFIMA fits.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec()
mspec = multispec( replicate(spec, n = 4) )
fitlist = multifit(multispec = mspec, data = dji30ret[,1:4])

## End(Not run)

Description

Method for multiple forecasting from a variety of univariate GARCH and ARFIMA models.

Usage

multiforecast(multifitORspec, data = NULL, n.ahead = 1, n.roll = 0, 
out.sample = 0, external.forecasts = list(mregfor = NULL, vregfor = NULL), 
cluster = NULL, ...)

Arguments

Value

A uGARCHmultiforecast or ARFIMAmultiforecast object containing details of the multiple GARCH or ARFIMA forecasts. See the class for details.

Author(s)

Alexios Ghalanos

Description

Method for creating a univariate multiple GARCH or ARFIMA specification object prior to fitting.

Usage

multispec( speclist )

Arguments

Value

A uGARCHmultispec or ARFIMAmultispec object containing details of the multiple GARCH or ARFIMA specifications.

Author(s)

Alexios Ghalanos

Examples

# how to make a list with 2 uGARCHspec objects of the same type
spec = ugarchspec()
mspec = multispec( replicate(2, spec) )
# note that replicate(spec, 2) does not work...be careful about the order 
# else explicity name 'n' (i.e. n = 2)

# or simply combine disparate objects
spec1 = ugarchspec(distribution = "norm")
spec2 = ugarchspec(distribution = "std")
mspec = multispec( c( spec1, spec2 ) )

Description

Quantile for NIG and GH distributions in alpha, beta, delta, mu and lambda parametrizations.

Usage

qnig(p, alpha = 1, beta = 0, delta = 1, mu = 0)
qgh(p, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = 1)

Arguments

Details

For use internally by rmgarch.

Value

A vector

Author(s)

Alexios Galanos

Description

Highest Level Virtual Package Class to which all other classes belong.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "rGARCH" in the signature.

Author(s)

Alexios Ghalanos

Examples

showClass("rGARCH")

Description

Density, distribution function, quantile function, 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.

Usage

ddist(distribution = "norm", y, mu = 0, sigma = 1, lambda = -0.5, skew = 1, 
shape = 5)
pdist(distribution = "norm", q, mu = 0, sigma = 1, lambda = -0.5, skew = 1, 
shape = 5)
qdist(distribution = "norm", p, mu = 0, sigma = 1, lambda = -0.5, skew = 1, 
shape = 5)
rdist(distribution = "norm", n, mu = 0, sigma = 1, lambda = -0.5, skew = 1, 
shape = 5)
fitdist(distribution = "norm", x, control=list())
dskewness(distribution = "norm", skew = 1, shape = 5, lambda = -0.5)
dkurtosis(distribution = "norm", skew = 1, shape = 5, lambda = -0.5)
distplot(distribution = "snorm", skewbounds = NULL, shapebounds = NULL, 
		n.points = NULL)
skdomain(distribution = "nig", kurt.max = 30, n.points = 25, lambda = 1, 
plot = TRUE, legend = NULL)

Arguments

Details

For the “nig” and “ghyp” distributions, the shape, skew and lambda are transformed from the ‘zeta-rho’ to the ‘alpha-beta’ parametrization and then scaled by the mean and standard deviation. The fitting routines use the solnp solver and minimize the negative of the log-likelihood. The “dskewness” and “dkurtosis” functions take as inputs the distribution name, skew and shape parameters and return the skewneness and excess kurtosis of the distribution. The functions are not at present vectorized. The distplot provides illustrative plots (or surfaces) of skewness and kurtosis for any of the distributions supported (with the exception of the GH which has 2 shape and 1 skew parameters and hence is impractical to represent).

Value

d* returns the density, p* returns the distribution function, q* returns the quantile function, and r* generates random deviates,
all values are numeric vectors.

fitdist returns a list with the following components:

dskewness returns the skewness of the distribution. dkurtosis returns the excess kurtosis of the distribution. skdomain returns the authorized domain of the distribution.

Author(s)

Diethelm Wuertz for the Rmetrics R-port of the “norm”, “snorm”, “std”, “sstd”, “ged”, “sged” and “nig” distrbutions.
Rigby, R. A. and Stasinopoulos D. M for the JSU distribution in the gamlss package.
Alexios Ghalanos for rugarch implementation and higher moment distribution functions.

References

Johnson, N. L. 1954, Systems of frequency curves derived from the first law of Laplace, Trabajos de Estadistica, 5, 283–291.
Barndorff-Nielsen, O. E. 1995, Normal inverse Gaussian processes and the modeling of stock returns, mimeo: Univ.of Aarhus Denmark.
Fernandez C. and Steel, M.F.J. 1998, On Bayesian Modelling of Fat Tails and Skewness, Journal of the American Statistical Association, 359–371.

Description

The SP500 index closing value log return from 1987-03-10 to 2009-01-30 from yahoo finance.

Usage

data(sp500ret)

Format

A data.frame containing 1x5523 observations.

Source

Yahoo Finance

Description

The SPDR SP500 index open-close return and the realized kernel volatility for the period 2002-01-02 to 2008-08-29 from the paper of Hansen, Huang and Shek (2011). Used for illustrating the implementation of the Realized GARCH model in rugarch.

Usage

data(spyreal)

Format

An xts object.

Source

Journal of Applied Econometrics Data Archive

References

Hansen, P. R., Huang, Z., and Shek, H. H. (2012). Realized GARCH: a joint model for returns and realized measures of volatility. Journal of Applied Econometrics, 27(6), 877–906.

Description

Function for running the rugarch benchmark suite.

Usage

ugarchbench( benchmark = c("commercial", "published") )

Arguments

Details

Currently, 2 benchmark suites are available. The “commercial” option runs the standard GARCH, apARCH and gjrGARCH against a commercial based product and reports the results. The data for this bechmarks is “AA” in the dji30ret dataset. The “published” option is based on the published benchmark of Bollerslev and Ghysels for the standard and exponential GARCH models on the dmbp data.

Author(s)

Alexios Ghalanos

Source

‘http://www.stanford.edu/~clint/bench/index.htm’

References

Brooks, C. 1997, GARCH Modelling in Finance: A review of the Software Options, Economic Journal, 107(443), 1271–1276.

Examples

## Not run: 
ugarchbench( benchmark = "published" )

## End(Not run)

Description

Class for the univariate GARCH Bootstrap based Forecasts.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHboot", directly. Class "rGARCH", by class "GARCHboot", distance 2.

Methods

as.data.frame

signature(x = "uGARCHboot"): extracts various values from object (see note).

plot

signature(x = "uGARCHboot", y = "missing"): bootstrap forecast plots.

show

signature(object = "uGARCHboot"): bootstrap forecast summary.

Note

The as.data.frame function takes optionally the arguments which, being either “sigma” or “series”, the argument type, with the options “raw” for the bootstrapped series, “summary” for summary statistics per n.ahead, and “q” for the quantiles of the n.ahead bootstrapped series, for which the option qtile is then required and takes a numeric vector of quantiles (e.g. c(0.05, 0.95) ).
The plot method provides for a Parameter Density Plots (only valid for the “full” method), and the series and sigma forecast plots with quantile error lines from the bootstrapped n.ahead distribution. The plot option which relates to either a numeric choice (1:3), an interactive choice (“ask” which is the default) and an all plot choice (“all”) for which only plots 2 and 3 are included.

Author(s)

Alexios Ghalanos

References

Pascual, L., Romo, J. and Ruiz, E. 2004, Bootstrap predictive inference for ARIMA processes, Journal of Time Series Analysis.
Pascual, L., Romo, J. and Ruiz, E. 2006, Bootstrap prediction for returns and volatilities in GARCH models, Computational Statistics and Data Analysis.

See Also

Classes uGARCHforecast, uGARCHfit and uGARCHspec.

Description

Method for forecasting the GARCH density based on a bootstrap procedures (see details and references).

Usage

ugarchboot(fitORspec, data = NULL, method = c("Partial", "Full"), 
sampling = c("raw", "kernel", "spd"), spd.options = list(upper = 0.9, 
lower = 0.1, type = "pwm", kernel = "normal"), n.ahead = 10, 
n.bootfit = 100, n.bootpred = 500, out.sample = 0, rseed = NA, solver = "solnp", 
solver.control = list(), fit.control = list(), 
external.forecasts = list(mregfor = NULL, vregfor = NULL), mexsimdata = NULL, 
vexsimdata = NULL, cluster = NULL, verbose = FALSE)

Arguments

Details

There are two main sources of uncertainty about n.ahead forecasting from GARCH models, namely that arising from the form of the predictive density and due to parameter estimation. The bootstrap method considered here, is based on resampling innovations from the empirical distribution of the fitted GARCH model to generate future realizations of the series and sigma. The “full” method, based on the referenced paper by Pascual et al (2006), takes into account parameter uncertainty by building a simulated distribution of the parameters through simulation and refitting. This process, while more accurate, is very time consuming which is why choice of parallel computation via a cluster (as in the ugarchdistribution is available and recommended). The “partial” method, only considers distribution uncertainty and while faster, will not generate prediction intervals for the sigma 1-ahead forecast for which only the parameter uncertainty is relevant in GARCH type models.
If using external regressors, the routine requires both the forecast (of length n.ahead as in the ugarchforecast routine) and a list of simulated forecasts as in the ugarchsim routine (else with be assumed zero). Finally, it is possible to resample based on 3 schemes, namely the “raw” innovations as in the original paper of Pascual et al (2006), “kernel” fits a Gaussian kernel to the innovations from the ks package in order to then generate random samples, and the “spd” fits a semi-parametric distribution to the innovations based on the spd package in order to generate the random samples, for which an optional list (spd.options) may be further passed to the spd fitting routine.

Value

A uGARCHboot object containing details of the GARCH bootstrapped forecast density.

Author(s)

Alexios Ghalanos

References

Pascual, L., Romo, J. and Ruiz, E. 2004, Bootstrap predictive inference for ARIMA processes, Journal of Time Series Analysis.
Pascual, L., Romo, J. and Ruiz, E. 2006, Bootstrap prediction for returns and volatilities in GARCH models, Computational Statistics and Data Analysis.

See Also

For specification ugarchspec, fitting ugarchfit, filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution.

Examples

## Not run: 
data(dji30ret)
spec = ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,1)), 
		mean.model=list(armaOrder=c(1,1), arfima=FALSE, include.mean=TRUE, 
		archm = FALSE, archpow = 1), distribution.model="std")
ctrl = list(tol = 1e-7, delta = 1e-9)
fit = ugarchfit(data=dji30ret[, "BA", drop = FALSE], out.sample = 0, 
				spec = spec, solver = "solnp", solver.control = ctrl,
				fit.control = list(scale = 1))
bootpred = ugarchboot(fit, method = "Partial", n.ahead = 120, n.bootpred = 2000)
bootpred
# as.data.frame(bootpred, which = "sigma", type = "q", qtile = c(0.01, 0.05))

## End(Not run)

Description

Class for the univariate GARCH Parameter Distribution.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHdistribution", directly. Class "rGARCH", by class "GARCHdistribution", distance 2.

Methods

as.data.frame

signature(x = "uGARCHdistribution"): Extracts various values from object (see note).

plot

signature(x = "uGARCHdistribution", y = "missing"): Parameter Distribution Plots.

show

signature(object = "uGARCHdistribution"): Parameter Distribution Summary.

Note

The as.data.frame function takes optionally 2 additional arguments, namely window which indicates the particular distribution window number for which data is required (is usually just 1 unless the recursive option was used), and which indicating the type of data required. Valid values for the latter are “rmse” for the root mean squared error between simulation fit and actual parameters, “stats” for various statistics computed for the simulations such as log likelihood, persistence, unconditional variance and mean, “coef” for the estimated coefficients (i.e. the parameter distribution and is the default choice), and “coefse” for the estimated robust standard errors of the coefficients (i.e. the parameter standard error distribution).
The plot method offers 4 plot types, namely, Parameter Density Plots (take window as additional argument), Bivariate Plots (take window as additional argument), Stats and RMSE (only when recursive option used) Plots. The standard option for which is used, allowing for a numeric arguments to one of the four plot types else interactive choice via “ask”.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHforecast, uGARCHfit and uGARCHspec.

Examples

## Not run: 
data(sp500ret)
spec = ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,1)), 
		mean.model=list(armaOrder=c(1,1), arfima=FALSE, include.mean=TRUE, 
		archm = FALSE, archpow = 1), distribution.model="std")
		
fit = ugarchfit(data=sp500ret[, 1, drop = FALSE], out.sample = 0, 
				spec = spec, solver = "solnp")
	
dist = ugarchdistribution(fit, n.sim = 2000, n.start = 50, m.sim = 5)

## End(Not run)

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.

Usage

ugarchdistribution(fitORspec, n.sim = 2000, n.start = 1, 
m.sim = 100,  recursive = FALSE, recursive.length = 6000, recursive.window = 1000,
presigma = NA, prereturns = NA, preresiduals = NA, rseed = NA,
custom.dist = list(name = NA, distfit = NA), mexsimdata = NULL, vexsimdata = NULL, 
fit.control = list(), solver = "solnp", solver.control = list(), cluster = NULL, ...)

Arguments

Details

This method facilitates the simulation and evaluation of the uncertainty of GARCH model parameters. The recursive option also allows the evaluation of the simulation based consistency (in terms of sqrt(N) ) of the parameters as the length (n.sim) of the data increases, in the sense of the root mean square error (rmse) of the difference between the simulated and true (hypothesized) parameters.
This is a very expensive function, particularly if using the recursive option, both on memory and cpu resources, performing many re-fits of the simulated data in order to generate the parameter distribution and it is therefore suggested that, if available, the parallel functionality should be used (in a system with ideally many cores and at least 4GB of RAM for the recursion option...).

Value

A uGARCHdistribution object containing details of the GARCH simulated parameters distribution.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec, fitting ugarchfit, filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, bootstrap forecast ugarchboot.

Description

Class for the univariate GARCH filter.

Extends

Class "GARCHfilter", directly. Class "rGARCH", by class "GARCHfilter", distance 2.

Methods

fitted

signature(object = "uGARCHfilter"): Extracts the fitted values.

residuals

signature(object = "uGARCHfilter"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

sigma

signature(object = "uGARCHfilter"): Extracts the conditional sigma values.

coef

signature(object = "uGARCHfilter"): Extracts the coefficients.

infocriteria

signature(object = "uGARCHfilter"): Calculates and returns various information criteria.

newsimpact

signature(object = "uGARCHfilter"): Calculates and returns the news impact curve.

likelihood

signature(object = "uGARCHfilter"): Extracts the likelihood.

signbias

signature(object = "uGARCHfilter"): Calculates and returns the sign bias test of Engle and Ng (1993).

gof

signature(object = "uGARCHfilter", 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). Groups is a numeric vector of bin sizes.

persistence

signature(object = "uGARCHfilter", pars = "missing", distribution = "missing", model = "missing", submodel = "missing"): Calculates and returns the persistence of the garch filter model.

halflife

signature(object = "uGARCHfilter", pars = "missing", distribution = "missing", model = "missing"): Calculates and returns the halflife of the garch fit variance given a uGARCHfilter object.

uncmean

signature(object = "uGARCHfilter"): Calculates and returns the unconditional mean of the conditional mean equation (constant, ARMAX, arch-in-mean).

uncvariance

signature(object = "uGARCHfilter", pars = "missing", distribution = "missing", model = "missing", submodel = "missing"): Calculates and returns the long run unconditional variance of the garch filter given a uGARCHfilter object.

quantile

signature(x = "uGARCHfilter"): Calculates and returns, given a vector of probabilities (additional argument “probs”), the conditional quantiles of the filtered object (x).

pit

signature(object = "uGARCHfilter"): Calculates and returns the conditional probability integral transform given the data and estimated density.

plot

signature(x = "uGARCHfilter", y = "missing"): Filter plots

show

signature(object = "uGARCHfilter"): Filter summary.

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.e the optimization process) such as the nyblom test.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
data(dji30ret)
ctrl = list(rho = 1, delta = 1e-8, outer.iter = 100, inner.iter = 650, 
tol = 1e-6)
spec = ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1)), 
		mean.model = list(armaOrder = c(1,1), include.mean = TRUE), 
		distribution.model = "std")
sgarch.fit = ugarchfit(data = dji30ret[,"AA",drop=FALSE], spec = spec, 
		solver = "solnp", solver.control = ctrl)
		
spec = ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1)), 
		mean.model = list(armaOrder = c(1,1), include.mean = TRUE), 
		distribution.model = "std", fixed.pars = as.list(coef(sgarch.fit)))
sgarch.filter = ugarchfilter(data = dji30ret[,"AA",drop=FALSE], spec = spec)

c(likelihood(sgarch.filter), likelihood(sgarch.fit))
c(uncmean(sgarch.filter), uncmean(sgarch.fit))
c(uncvariance(sgarch.filter), uncvariance(sgarch.fit))

## End(Not run)

Description

Method for filtering a variety of univariate GARCH models.

Usage

ugarchfilter(spec, data, out.sample = 0, n.old=NULL, rec.init = 'all',
trunclag = 1000, ...)

Arguments

Details

The n.old argument is optional and indicates the length of the original data (in cases when this represents a series augmented by newer data). 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. 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.

Value

A uGARCHfilter object containing details of the GARCH filter.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec, fitting ugarchfit, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

## Not run: 
data(sp500ret)
ctrl = list(RHO = 1,DELTA = 1e-8,MAJIT = 100,MINIT = 650,TOL = 1e-6)
spec = ugarchspec(variance.model = list(model = "eGARCH", garchOrder = c(1,1)),
		mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
		distribution.model = "std")
egarch.fit = ugarchfit(data = sp500ret[,1,drop=FALSE], spec = spec,
		solver = "solnp", solver.control = ctrl)

spec = ugarchspec(variance.model = list(model = "eGARCH", garchOrder = c(1,1)),
		mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
		distribution.model = "std", fixed.pars = as.list(coef(egarch.fit)))
egarch.filter = ugarchfilter(data = sp500ret[,1,drop=FALSE], spec = spec)

## End(Not run)

Description

Class for the univariate GARCH fit.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class GARCHfit, directly. Class rGARCH, by class GARCHfit, distance 2.

Slots

fit:

Object of class "vector" Holds data on the fitted model.

model:

Object of class "vector" The model specification common to all objects.

Methods

coef

signature(object = "uGARCHfit"): Extracts the coefficients.

cofint

signature(object = "uGARCHfit"): Similar to the stats S3 method confint, extracts coefficient confidence intervals taking additional optional arguments parm and level, as well as robust (default: FALSE) indicating whether to use the robust covariance matrix for the calculations.

vcov

signature(object = "uGARCHfit"): Extracts the covariance matrix of the parameters. Additional logical option of ‘robust’ indicates whether to extract the robust based covariance matrix.

infocriteria

signature(object = "uGARCHfit"): Calculates and returns various information criteria.

nyblom

signature(object = "uGARCHfit"): Calculates and returns the Hansen-Nyblom stability test (1990).

gof

signature(object = "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). Groups is a numeric vector of bin sizes.

newsimpact

signature(object = "uGARCHfit"): Calculates and returns the news impact curve.

signbias

signature(object = "uGARCHfit"): Calculates and returns the sign bias test of Engle and Ng (1993).

likelihood

signature(object = "uGARCHfit"): Extracts the likelihood.

sigma

signature(object = "uGARCHfit"): Extracts the conditional sigma values.

fitted

signature(object = "uGARCHfit"): Extracts the fitted values.

residuals

signature(object = "uGARCHfit"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

getspec

signature(object = "uGARCHfit"): Extracts and returns the GARCH specification from a fit object.

uncvariance

signature(object = "uGARCHfit", pars = "missing", distribution="missing", model = "missing", vexdata = "missing"): Calculates and returns the long run unconditional variance of the GARCH fit given a uGARCHfit object.

uncvariance

signature(object = "missing", pars = "numeric", distribution = "character", model = "character", submodel = "ANY", vexdata = "ANY"): Calculates and returns the long run unconditional variance of the GARCH fit given a named parameter vector as returned by the fit, 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.

uncmean

signature(object = "uGARCHfit"): Calculates and returns the unconditional mean of the conditional mean equation (constant, ARMAX, arch-in-mean).

persistence

signature(object = "uGARCHfit", pars = "missing", distribution = "missing", model = "missing"): Calculates and returns the persistence of the GARCH fit model given a uGARCHfit object.

persistence

signature(object = "missing", pars = "numeric", distribution = "character", model = "character"): Calculates and returns the persistence of the GARCH fit model given a named parameter vector as returned by the fit, a distribution model name and a GARCH model name with a submodel included if the model is of the nested type such as fGARCH.

halflife

signature(object = "uGARCHfit", pars = "missing", distribution = "missing", model = "missing"): Calculates and returns the halflife of the GARCH fit variance given a uGARCHfit object.

halflife

signature(object = "missing", pars = "numeric", distribution = "character", model = "character"): Calculates and returns the halflife of the GARCH fit variance given a named parameter vector as returned by the fit, a distribution model name and a GARCH model name with a submodel included if the model is of the nested type such as fGARCH.

convergence

signature(object = "uGARCHfit"): Returns the solver convergence code for the fitted object (zero denotes convergence).

quantile

signature(x = "uGARCHfit"): Calculates and returns, given a vector of probabilities (additional argument “probs”), the conditional quantiles of the fitted object (x).

pit

signature(object = "uGARCHfit"): Calculates and returns the conditional probability integral transform given the data and estimated density.

reduce

signature(object = "uGARCHfit"): Zeros parameters (fixing to zero in rugarch is equivalent to eliminating them in estimation) with p-values (optional argument “pvalue”) greater than 0.1 (default), and re-estimates the model. Additional arguments are passed to ugarchfit.An additional option “use.robust” (default TRUE) asks whether to use the robust calculated p-values.

plot

signature(x = "uGARCHfit", y = "missing"): Fit plots.

show

signature(object = "uGARCHfit"): Fit summary.

Note

Methods for coef, likelihood, fitted, sigma and residuals provide extractor functions for those values.
Method for show gives detailed summary of GARCH fit with various tests.
Method for plot provides for interactive choice of plots, 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”).
The infocriteria method calculates and returns the information criteria (AIC, BIC etc) of the GARCH fit.
The nyblom method calculates and returns the Hansen-Nyblom joint and individual coefficient stability test statistic and critical values.
The gof methods calculates and returns the adjusted goodness of fit statistic and p-values for the fitted distribution. The groups parameter is a numeric vector of grouped bin sizes for the test. See the references in the package introduction for the original paper by Vlaar and Palm explaining the test.
The signbias methods calculates and returns the sign bias test of Engle and Ng (see the references in the package introduction).
Methods for calculating and extracting persistence, 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), a distribution name and the GARCH model (with submodel argument for the fGARCH model).
Unconditional mean and variance of the model may be extracted by means of the uncmean and uncvariance methods. The uncvariance may take either a fit object or a named parameter list, distribution and GARCH model name. The uncmean will only take a fit object due to the complexity of the calculation requiring much more information than the uncoditional variance.
The news impact method returns a list with the calculated values (zx, zy) and the expression (xexpr, yexpr) which can be used to illustrate the plot.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHforecast, uGARCHsim and uGARCHspec.

Examples

## Not run: 
# Basic GARCH(1,1) Spec
data(dmbp)
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec)
fit
# object fit:
slotNames(fit)
# sublist fit@fit
names(fit@fit)
coef(fit)
infocriteria(fit)
likelihood(fit)
nyblom(fit)
signbias(fit)
head(sigma(fit))
head(residuals(fit))
head(fitted(fit))
gof(fit,c(20,30,40,50))
uncmean(fit)
uncvariance(fit)
#plot(fit,which="all")
# news impact example
spec = ugarchspec(variance.model=list(model="apARCH"))
fit = ugarchfit(data = dmbp[,1], 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.
ni=newsimpact(z = NULL, fit)
#plot(ni$zx, ni$zy, ylab=ni$yexpr, xlab=ni$xexpr, type="l", main = "News Impact Curve")

## End(Not run)

Description

Method for fitting a variety of univariate GARCH models.

Usage

ugarchfit(spec, data, out.sample = 0, solver = "solnp", solver.control = list(),
fit.control = list(stationarity = 1, fixed.se = 0, scale = 0, rec.init = 'all',
trunclag = 1000),
numderiv.control = list(grad.eps=1e-4, grad.d=0.0001,
grad.zero.tol=sqrt(.Machine$double.eps/7e-7), hess.eps=1e-4, hess.d=0.1,
hess.zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2),...)

Arguments

Details

The GARCH optimization routine first calculates a set of feasible starting points which are used to initiate the GARCH recursion. The main part of the likelihood calculation is performed in C-code for speed.
The out.sample option is provided in order to carry out forecast performance testing against actual data. A minimum of 5 data points are required for these tests. If the out.sample option is positive, then the routine will fit only N - out.sample (where N is the total data length) data points, leaving out.sample points for forecasting and testing using the forecast performance measures. In the ugarchforecast routine the n.ahead may also be greater than the out.sample number resulting in a combination of out of sample data points matched against actual data and some without, which the forecast performance tests will ignore.
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). The solver.control list then accepts the following additional (to the solnp) arguments: “n.restarts” is the number of solver restarts required (defaults to 1), “parallel” (logical), “pkg” (either snowfall or multicore) and “cores” (the number of cores or workers to use) for use of parallel functionality, “rseed” is the seed to initialize the random number generator, and “n.sim” is the number of simulated parameter vectors to generate per n.restarts.
The “hybrid” strategy solver first tries the “solnp” solver, in failing to converge then tries then “nlminb”, the “gosolnp” and finally the “nloptr” solvers. Solver control parameters can be passed for all the solvers in the solver.control list as one long list which will be filtered for each solver's specific options as and when that solver is called during the hybrid strategy optimization. It is still possible that the Hessian at the optimal found cannot be inverted, in which case a warning is printed and there will not be any standard errors. In this case it is suggested that the problem is re-run with different solver parameters. It is also possible that the solution, while still ‘almost’ optimal may be at a saddle-point very near the global optimum in which case the Hessian may still be invertible but one eigenvalue is negative. The uGARCHfit object has a value in the fit slot called condH (object@fit$condH) which indicates the approximate number of decimal places lost to roundoff/numerical estimation error. When this is NaN, this indicates the case just described of one negative eigenvalue/saddlepoint (this previously flagged a warning but is now silenced and it is upto to the user to decide whether it is worth investigating further).

Value

A uGARCHfit object containing details of the GARCH fit.

Note

The nloptr solver takes the following options in the solver.control list:

The solver option for nloptr has 10 different choices (1:10), which are 1:‘COBYLA’, 2:‘BOBYQA’, 3:‘PRAXIS’, 4:‘NELDERMEAD’, 5:‘SBPLX’, 6:‘AUGLAG’+‘COBYLA’, 7:‘AUGLAG’+‘BOBYQA’, 8:‘AUGLAG’+‘PRAXIS’, 9:‘AUGLAG’+‘NELDERMEAD’ and 10:‘AUGLAG’+‘SBPLX’. As always, your mileage will vary and care should be taken on the choice of solver, tuning parameters etc. If you do use this solver try 9 or 10 first.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec,filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

# Basic GARCH(1,1) Spec
data(dmbp)
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec)
fit
coef(fit)
head(sigma(fit))
#plot(fit,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[,1], spec = spec, out.sample=100)
forc = ugarchforecast(fit, n.ahead=100)
# this means that 100 data points are left from the end with which to
# make inference on the forecasts
fpm(forc)

Description

Class for the univariate GARCH forecast.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class GARCHforecast, directly. Class rGARCH, by class GARCHforecast, distance 2.

Methods

sigma

signature(x = "uGARCHforecast"): The n.ahead by n.roll+1 matrix of conditional sigma forecasts. The column names are the T[0] dates.

fitted

signature(x = "uGARCHforecast"): The n.ahead by n.roll+1 matrix of conditional mean forecasts. The column names are the T[0] dates.

quantile

signature(x = "uGARCHforecast"): Calculates and returns, given a scalar for the probability (additional argument “probs”), the conditional quantile of the forecast object as an n.ahead by n.roll+1 matrix (with the same type of headings as the sigma and fitted methods).

plot

signature(x = "uGARCHforecast", y = "missing"): Forecast plots with n.roll optional argument indicating the rolling sequence to plot.

fpm

signature(object = "uGARCHforecast"): Forecast performance measures.

show

signature(object = "uGARCHforecast"): Forecast summary returning the 0-roll frame only.

Note

Since versions 1.01-3, a sigma and fitted methods have been introduced which extract the n.ahead by (n.roll+1) matrix of conditional sigma and mean forecasts respectively, with column names the T[0] time index. This is unlike the old data.frame which returned the T+1 etc dates. These two methods are the default extractors in rugarch (used on estimated, filtered, forecast and simulation class objects) and the other methods, namely as.data.frame is now deprecated with the exception of a few classes where it is still used (uGARCHdistribution, uGARCHboot and uGARCHroll).
The plot method takes additional arguments which and n.roll indicating which roll frame to plot.
The fpm method returns the Mean Squared Error (MSE), Mean Absolute Error (MAE), Directional Accuracy (DAC) and number of points used for the calculation (N), of forecast versus realized returns, if the extra summary option is set to TRUE (default). This is a 4 x (n.roll+1) matrix, with row headings the T[0] time index, and requires at least 5 points to calculate the summary measures else will return NA. When n.ahead>1, this method calculates the measures on the n.ahead>1 unconditional forecast, but if n.ahead=1 with n.roll>4, it will calculate the measures on the rolling forecast instead. Finally, when summary is set to FALSE, the method will return a list of length n.roll+1 of xts objects with the loss functions (Squared Error and Absolute Error and Directional Hits).

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHfit, uGARCHsim and uGARCHspec.

Examples

## Not run: 
# Basic GARCH(1,1) Spec
data(dmbp)
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec, out.sample = 100)
forc1 = ugarchforecast(fit, n.ahead=100, n.roll = 100)
forc
#plot(forc, which = "all")

## End(Not run)

Description

Method for forecasting from a variety of univariate GARCH models.

Usage

ugarchforecast(fitORspec, data = NULL, n.ahead = 10, n.roll = 0, out.sample = 0,
		external.forecasts = list(mregfor = NULL, vregfor = NULL),
		trunclag = 1000, ...)

Arguments

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 a specification object (in which case the data is required) with fixed parameters.
The forecast is based on the expected value of the innovations and hence the density chosen. One step ahead forecasts are based on the value of the previous data, while n-step ahead (n>1) are based on the unconditional expectation of the models.
The ability to roll the forecast 1 step at a time is implemented with the n.roll argument which controls how many times to roll the n.ahead forecast. The default argument of n.roll = 0 denotes no rolling and returns the standard n.ahead forecast. Critically, since n.roll depends on data being available from which to base the rolling forecast, the ugarchfit function needs to be called with the argument out.sample being at least as large as the n.roll argument, or in the case of a specification being used instead of a fit object, the out.sample argument directly in the forecast function.

Value

A uGARCHforecast object containing details of the GARCH forecast. See the class for details on the returned object and methods for accessing it and performing some tests.

Author(s)

Alexios Ghalanos

See Also

For filtering ugarchfilter,simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

## Not run: 
# Basic GARCH(1,1) Spec
data(dmbp)
spec = ugarchspec()
fit = ugarchfit(data = dmbp[,1], spec = spec)
forc = ugarchforecast(fit, n.ahead=20)
forc
head(sigma(forc))
head(fitted(forc))
#plot(forc,which="all")

## End(Not run)

Description

Class for the univariate GARCH Multiple filter.

Extends

Class "GARCHfilter", directly. Class "rGARCH", by class "GARCHfilter", distance 3.

Methods

fitted

signature(object = "uGARCHmultifilter"): Extracts the fitted values.

residuals

signature(object = "uGARCHmultifilter"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

sigma

signature(object = "uGARCHmultifilter"): Extracts the conditional sigma values.

coef

signature(object = "uGARCHmultifilter"): Extracts the coefficients.

likelihood

signature(object = "uGARCHmultifilter"): Extracts the likelihood.

show

signature(object = "uGARCHmultifilter"): Filter summary.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHmultiforecast, uGARCHmultifit and uGARCHmultispec.

Description

Class for the univariate GARCH Multiple fit.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class GARCHfit, directly. Class rGARCH, by class GARCHfit, distance 3.

Methods

coef

signature(object = "uGARCHmultifit"): Extracts the coefficients.

likelihood

signature(object = "uGARCHmultifit"): Extracts the likelihood.

sigma

signature(object = "uGARCHmultifit"): Extracts the conditional sigma values.

fitted

signature(object = "uGARCHmultifit"): Extracts the fitted values.

residuals

signature(object = "uGARCHmultifit"): Extracts the residuals. Optional logical argument standardize (default is FALSE) allows to extract the standardized residuals.

show

signature(object = "uGARCHmultifit"): Fit summary.

Note

Methods for coef, likelihood, fitted, sigma and residuals provide extractor functions for those values.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHmultiforecast, uGARCHmultispec and uGARCHmultifilter.

Description

Class for the univariate GARCH Multiple forecast.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class GARCHforecast, directly. Class rGARCH, by class GARCHforecast, distance 3.

Methods

sigma

signature(x = "uGARCHmultiforecast"): extracts the n.ahead by (n.roll+1) by n.assets array of conditional sigma forecasts.

fitted

signature(x = "uGARCHforecast"): extracts the n.ahead by (n.roll+1) by n.assets array of conditional mean forecasts.

show

signature(object = "uGARCHforecast"): forecast summary.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHmultifilter, uGARCHmultifit and uGARCHmultispec.

Description

Class for the univariate GARCH Multiple specification.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "GARCHspec", directly. Class "rGARCH", by class "GARCHspec", distance 3.

Methods

show

signature(object = "uGARCHmultispec"): specification summary.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHmultiforecast, uGARCHmultifit and uGARCHmultifilter.

Description

Class for the univariate GARCH Path simulation.

Objects from the Class

A virtual Class: No objects may be created from it.

Extends

Class "uGARCHpath", directly. Class "rGARCH", by class "GARCHpath", distance 2.

Methods

sigma

signature(object = "uGARCHpath"): Extracts the conditional sigma simulated values as a matrix of size n.sim x m.sim.

fitted

signature(object = "uGARCHpath"): Extracts the conditional mean simulated values as a matrix of size n.sim x m.sim.

quantile

signature(x = "uGARCHpath"): Calculates and returns, given a scalar for the probability (additional argument “probs”), the conditional quantile of the simulated object as an n.sim by m.sim matrix (with the same type of headings as the sigma and fitted methods).

plot

signature(x = "uGARCHpath", y = "missing"): path simulation plots.

show

signature(object = "uGARCHpath"): path simulation summary.

Note

The sigma and fitted methods are used to extract the matrix of simulated conditional sigma and mean values. The as.data.frame method is globally deprecated as an extractor method in rugarch with the exception of a few classes which still makes sense to use them.

Author(s)

Alexios Ghalanos

See Also

Classes uGARCHsim, uGARCHfit and uGARCHspec.

Description

Method for simulating the path of a GARCH model from a variety of univariate GARCH models. This is a convenience function which does not require a fitted object (see note below).

Usage

ugarchpath(spec, n.sim=1000, n.start=0, m.sim=1, presigma=NA, prereturns=NA,
preresiduals=NA, rseed=NA, custom.dist=list(name=NA,distfit=NA), mexsimdata=NULL,
vexsimdata=NULL, trunclag=1000, ...)

Arguments

Details

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. Instead, a GARCH spec object is required with the fixed model parameters. The mcsGARCH model is not supported for the path method-use ugarchsim instead.

Value

A uGARCHpath object containing details of the GARCH path simulation.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec, fitting ugarchfit, filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, rolling forecast and estimation ugarchroll, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

## Not run: 
# create a basic sGARCH(1,1) spec:
spec=ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),
		mean.model=list(armaOrder=c(0,0), include.mean=TRUE, garchInMean =
		FALSE, inMeanType = 2), distribution.model="sstd",
		fixed.pars=list(mu=0.001,omega=0.00001, alpha1=0.05, beta1=0.90,
		shape=4,skew=2))
# simulate the path
path.sgarch = ugarchpath(spec, n.sim=3000, n.start=1, m.sim=1)

## End(Not run)

Description

Class for the univariate GARCH rolling forecast.

Slots

forecast:

Object of class "vector"

model:

Object of class "vector"

Extends

Class "GARCHroll", directly. Class "rGARCH", by class "GARCHroll", distance 2.

Methods

as.data.frame

signature(x = "uGARCHroll"): Extracts various values from object (see note).

plot

signature(x = "uGARCHroll", y = "missing"): Roll result backtest plots (see note).

report

signature(object = "uGARCHroll"): Roll backtest reports (see note).

resume

signature(object = "uGARCHroll"): Resumes a rolling backtest which has non-converged windows using alternative solver and control parameters.

fpm

signature(object = "uGARCHroll"): Forecast performance measures.

coef

signature(object = "uGARCHroll"): Extracts the list of coefficients for each estimated window in the rolling backtest.

quantile

signature(x = "uGARCHroll"): Calculates and returns, given a vector of probabilities (additional argument “probs”), the conditional quantiles of the rolling object as an xts matrix.

pit

signature(object = "uGARCHroll"): Calculates and returns the conditional probability integral transform given the realized data and forecast density.

convergence

signature(object = "uGARCHroll"): Returns the convergence code for the estimation windows, with 0 indicating that all have converged and 1 that there were non-converged windows. In the latter case the ‘nonconverged’ attribute is also printed of those windows which failed to converge.

show

signature(object = "uGARCHroll"): Summary.

Note

The as.data.frame extractor method allows the extraction of either the conditional forecast density or the VaR. It takes additional argument which with valid values either “density” or “VaR”.
The coef method will return a list of the coefficients and their robust standard errors (assuming the keep.coef argument was set to TRUE in the ugarchroll function), and the ending date of each estimation window.
The plot method takes the following additional arguments:
1.which allows for either a numeric value of 1:4, else will default to “ask” for interactive printing of the options in the command windows. Additionally, the value of “all” wil create a 2x2 chart with all plots.
2.VaR.alpha for the Value at Risk backtest plot, this is the tail probability and defaults to 0.01.
3.density.support the support for the time varying density plot density, defaults to c(-0.15, 0.15) but you should change this to something more appropriate for your data and period under consideration.
The report method takes the following additional arguments:
1.type for the report type. Valid values are “VaR” for the VaR report based on the unconditional and conditional coverage tests for exceedances (discussed below) and “fpm” for forecast performance measures.
2.VaR.alpha (for the VaR backtest report) is the tail probability and defaults to 0.01.
3.conf.level the confidence level upon which the conditional coverage hypothesis test will be based 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 method (separately from report) takes additional logical argument summary, which when TRUE will return the mean squared error (MSE), mean absolute error (MAE) and directional accuracy of the forecast versus realized returns. When FALSE, it will return a data.frame of the time series of squared (SE) errors, absolute errors (AE), directional hits (HITS), and a VaR Loss function described in Gonzalez-Rivera, Lee, and Mishra (2004) for each coverage level where it was calculated. This can then be compared, with the VaR loss of competing models using such tests as the model confidence set (MCS) of Hansen, Lunde and Nason (2011).

Author(s)

Alexios Ghalanos

Description

Method for creating rolling density forecast from ARMA-GARCH models with option for refitting every n periods with parallel functionality.

Usage

ugarchroll(spec, data, n.ahead = 1, forecast.length = 500, 
n.start = NULL, refit.every = 25, refit.window = c("recursive", "moving"), 
window.size = NULL, solver = "hybrid", fit.control = list(), 
solver.control = list(), calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.05), 
cluster = NULL, keep.coef = TRUE, ...)

Arguments

Details

This is a wrapper function for creating rolling forecasts of the conditional GARCH density, and optionally calculating the Value at Risk at specified levels. The argument refit.every determines every how many periods the model is re-estimated. Given a dataset of length N, it is possible to choose either how many periods from the end to use for out of sample forecasting (using the forecast.length option), or the starting point for initializing the rolling forecast (and using all the data after that for the out of sample forecast). Only rolling 1-ahead forecasts are supported spanning the dataset, which should be useful for backtesting models. Anything more complicated should be wrapped by the user by making use of the underlying functions in the package. The function has 2 main methods for viewing the data, a standard plot method and a report methods (see class uGARCHroll for details on how to use these methods). In case of no-convergence in some of all the windows, a new method called resume now allows to pass the returned (non-converged) object with new solver and control parameters to be re-estimated (only the non-converged windows are re-estimated). Non-convergence here implies both a failure of the solver to converge to a solution (global failure) OR a failure to invert the resulting Hessian (local failure). The convergence method can be used on an object (aside from the printed warning) to print out the number of the non-converged estimation windows.
Parallel functionality is now based entirely on the parallel package, and it is up to the user to pass a cluster object, and then stop it once the routine is completed.

Value

An object of class uGARCHroll.

Author(s)

Alexios Ghalanos

See Also

For specification ugarchspec, fitting ugarchfit, filtering ugarchfilter, forecasting ugarchforecast, simulation ugarchsim, parameter distribution and uncertainty ugarchdistribution, bootstrap forecast ugarchboot.

Examples

## Not run: 
data(sp500ret)
spec = ugarchspec(distribution.model = "std")
mod = ugarchroll(spec, data = sp500ret, n.ahead = 1, 
n.start = 1000,  refit.every = 500, refit.window = "recursive", 
solver = "hybrid", fit.control = list(),
calculate.VaR = TRUE, VaR.alpha = c(0.01, 0.025, 0.05),
keep.coef = TRUE)
report(mod, type="VaR", VaR.alpha = 0.01, conf.level = 0.95) 
report(mod, type="fpm")

## End(Not run)

Description

Class for the univariate GARCH simulation.

Extends

Class "GARCHsim", directly. Class "rGARCH", by class "GARCHsim", distance 2.

Slots

simulation:

Object of class "vector" Holds data on the simulation.

model:

Object of class "vector" The model specification common to all objects.

seed:

Object of class "integer" The random seed used.