mlgarch: Estimate a multivariate CCC-log-GARCH(1,1) model
In lgarch: Simulation and Estimation of Log-GARCH Models

Description Usage Arguments Value Note Author(s) References See Also Examples

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

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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)

`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

A list of class 'mlgarch'

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

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/

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

##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)