lgarch (version 0.6-2)

mlgarch: Estimate a multivariate CCC-log-GARCH(1,1) model

Description

Fit a multivariate Constant Conditional Correlation (CCC) log-GARCH(1,1) model with multivariate Gaussian Quasi Maximum Likelihood (QML) via the VARMA representation, see Sucarrat, Gronneberg and Escribano (2013). Zero-values on y are treated as missing values, as suggested in Sucarrat and Escribano (2013). Estimation is via the nlminb function, whereas a numerical estimate of the Hessian is obtained with optimHess for the computation of the variance-covariance matrix

Usage

mlgarch(y, arch = 1, garch = 1, xreg = NULL, initial.values = NULL, lower = NULL, upper = NULL, nlminb.control = list(), vcov = TRUE, objective.penalty = NULL, solve.tol = .Machine$double.eps, c.code = TRUE)

Arguments

y

a numeric matrix, typically financial returns or regression errors

arch

the arch order (i.e. an integer equal to or greater than 0). The default is 1. NOTE: in the current version the order cannot be greater than 1

garch

the garch order (i.e. an integer equal to or greater than 0). The default is 1. NOTE: in the current version the order cannot be greater than 1

xreg

a vector or a matrix with the conditioning variables. The x-variables enter in each of the equations

initial.values

NULL (default) or a vector with the initial values of the VARMA representation

lower

NULL (default) or a vector with the lower bounds of the parameter space (of the VARMA representation). If NULL, then the values are automatically chosen

upper

NULL (default) or a vector with the upper bounds of the parameter space (of the VARMA representation). If NULL, then the values are automatically chosen

nlminb.control

list of control options passed on to the nlminb optimiser

vcov

logical. If TRUE (default), then the variance-covariance matrix is computed. The FALSE options makes estimation faster, but the variance-covariance matrix cannot be extracted subsequently

objective.penalty

NULL (default) or a numeric value. If NULL, then the log-likelihood value associated with the initial values is used. Sometimes estimation can result in NA and/or +/-Inf values (this can be fatal for simulations). The value objective.penalty is the value returned by the log-likelihood function lgarchObjective in the presence of NA or +/-Inf values

solve.tol

The function solve is used for the inversion of the Hessian in computing the variance-covariance matrix. The value solve.tol is passed on to solve, and is the tolerance for detecting linear dependencies in the columns

c.code

logical. TRUE (default) is (much) faster, since it makes use of compiled C-code

Value

References

Sucarrat and 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, Gronneberg and 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/

See Also

lgarchSim, coef.lgarch, fitted.lgarch, logLik.lgarch, print.lgarch, residuals.lgarch and vcov.lgarch

Examples

##simulate 1000 observations from a 2-dimensional
##ccc-log-garch(1,1) w/default parameter values:
set.seed(123)
y <- mlgarchSim(1000)

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

##print results:
print(mymod)

##extract ccc-log-garch coefficients:
coef(mymod)

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

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

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

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

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