lgarch-package {lgarch}

Simulation and estimation of log-GARCH models

Description

This package provides facilities for the simulation and estimation of univariate log-GARCH models, and for the multivariate CCC-log-GARCH(1,1) model, see Sucarrat, Gronneberg and Escribano (2013), Sucarrat and Escribano (2013), and Francq and Sucarrat (2013).

Let y[t] denote a financial return or the error of a regression at time t such that

y[t] = sigma[t]*z[t],

where sigma[t] > 0 is the conditional standard deviation or volatility at t, and where z[t] is an IID innovation with mean zero and unit variance. The log-volatility specifiction of the log-GARCH-X model is given by

ln sigma[t]^2 = intercept + Sum_i alpha_i * ln y[t-i]^2 + Sum_j beta_j *ln sigma[t-1]^2 + Sum_k lambda_k * x[t]_k,

where the conditioning x-variables can be contemporaneous and/or lagged. The lgarch package estimates this model via its ARMA-X representation, see Sucarrat, Gronneberg and Escribano (2013), and treats zeros on y as missing values, see Sucarrat and Escribano (2013).

Details

Package:	lgarch
Type:	Package
Version:	0.6-2
Date:	2015-09-14
License:	GPL-2
LazyLoad:	yes

The main functions of the package are: lgarchSim, mlgarchSim, lgarch and mlgarch. The first two functions simulate from a univariate and a multivariate log-GARCH model, respectively, whereas the latter two estimate a univariate and a multivariate log-GARCH model, respectively.

The lgarch and mlgarch functions return an object (a list) of class 'lgarch' and 'mlgarch', respectively. In both cases a collection of methods can be applied to each of them: coef, fitted, logLik, print, residuals, summary and vcov. In addition, the function rss can be used to extract the Residual Sum of Squares of the estimated ARMA representation from an lgarch object.

The output produced by the lgarchSim and mlgarchSim functions, and by the fitted and residuals methods, are of the Z's ordered observations (zoo) class, see Zeileis and Grothendieck (2005), and Zeileis, Grothendieck and Ryan (2014). This means a range of time-series and plotting methods are available for these objects.

Author(s)

Genaro Sucarrat, http://www.sucarrat.net/

References

Francq, C. and G. Sucarrat (2013), 'An Exponential Chi-Squared QMLE for Log-GARCH Models via the ARMA Representation', MPRA Paper 51783: http://mpra.ub.uni-muenchen.de/51783/

Sucarrat, G. and A. Escribano (2013), 'Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns', MPRA Paper 50699: http://mpra.ub.uni-muenchen.de/50699/

Sucarrat, G., S. Gronneberg and A. Escribano (2013), 'Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown', MPRA Paper 49344: http://mpra.ub.uni-muenchen.de/49344/

Zeileis, A. and G. Grothendieck (2005), 'zoo: S3 Infrastructure for Regular and Irregular Time Series', Journal of Statistical Software 14, pp. 1-27

Zeileis, A., G. Grothendieck, J.A. Ryan and F. Andrews(2014), 'zoo: S3 Infrastructure for Regular and Irregular Time Series (Z's ordered observations)', R package version 1.7-11, http://CRAN.R-project.org/package=zoo/

See Also

lgarchSim, mlgarchSim, lgarch, mlgarch, coef.lgarch, coef.mlgarch, fitted.lgarch,
fitted.mlgarch, logLik.lgarch, logLik.mlgarch, print.lgarch, print.mlgarch,
residuals.lgarch, residuals.mlgarch, rss, summary.mlgarch, summary.mlgarch, vcov.lgarch,
vcov.mlgarch and zoo

Examples

##simulate 500 observations w/default parameter values from
##a univariate log-garch(1,1):
set.seed(123)
y <- lgarchSim(500)

##estimate a log-garch(1,1):
mymod <- lgarch(y)

##print results:
print(mymod)

##extract coefficients:
coef(mymod)

##extract Gaussian log-likelihood (zeros excluded, if any) of the log-garch model:
logLik(mymod)

##extract Gaussian log-likelihood (zeros excluded, if any) of the arma representation:
logLik(mymod, arma=TRUE)

##extract variance-covariance matrix:
vcov(mymod)

##extract and plot the fitted conditional standard deviation:
sdhat <- fitted(mymod)
plot(sdhat)

##extract and plot standardised residuals:
zhat <- residuals(mymod)
plot(zhat)

##extract and plot all the fitted series:
myhat <- fitted(mymod, verbose=TRUE)
plot(myhat)

##simulate 1000 observations from a two-dimensional
##ccc-log-garch(1,1) w/default parameter values:
set.seed(123)
yy <- mlgarchSim(1000)

##estimate a 2-dimensional ccc-log-garch(1,1):
myymod <- mlgarch(yy)

##print results:
print(myymod)