Hi,

I would like to ask if was possible to implement in a function computing gradient in the fGarch package. Or is there a quick and easy way of implementing a gradient function so that I can do it myself? Based on the paper 'Parameter Estimation of ARMA Models with GARCH/APARCH Errors' by Wuertz, Chalabi and Luksan, I think that a function computing gradient was available for garch models in Rmetrics in the past. However, I did not find gradient in fGarch 260.72.
The reason for my question is that I would like to calculate robust covariance matrix (and robust standard errors) for a garch model estimated under the assumption of normally distributed standardised errors, for which I need hessian and gradient. The robust covariance matrix for such a QML estimator is computed as hessian^(-1)*OPG*hessian^(-1), where OPG is the outer product of the gradient, i.e. gradient*(transposed gradient). Clearly, hessian is available but I do not have the gradient.
Maybe the robust covariance matrix could be implemented at some point in the future along the following lines:

## robust works only for cond.dist == norm
if (cov.matrix == "robust") {
fit$cvar = solve(fit$hessian) %*% (gradient %o% gradient) %*% solve(fit$hessian)
} else {
fit$cvar = solve(fit$hessian) }


Thanks for your answer.

Best regards

Michal Miklovic




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