fGarch: possible bug(s) in ICS & LLH in summary

[chalabi at phys.ethz.ch]

Hi Michal,

I wanted to change the sign of the LLH in the output of garchFit for
some time now, but for whatever reason I never did it. 

Thanks for your helpful comments!

regards,
Yohan

michal miklovic <mmiklovic at yahoo.com> writes:

> Hi,
>
> I wanted to compare several garch models on the basis of information criteria statistics (ICS) and I found a possible bug, which affects a couple of computations in fGarch.
>
> First, I would suggest that the log likelihood in the summary function is reported as follows:
>
> LLH = (-1)*object at fit$value
>
> because it should be the value of maximised log likelihood (and not minimised negative log likelihood). The consequent discrepancy with the iteration path output could be solved by printing the following:
>
> cat("\nFinal Estimate of the Negative LLH:\n")
>
>
> Second, I would suggest changing the hessian and covariance matrices calculations to, respectively:
>
> fit$hessian = (-1)*.garch??DAHessian( ... )
>
> fit$cvar = (-1)*solve(fit$hessian)
>
> These changes would have no effect on the estimates of covariance matrix (and thus also standard errors) but the hessian matrix would correspond to a maximised log likelihood, which is currently not the case, and would have negative numbers on the diagonal, which is rather intuitive for a maximum.
>
>
> Finally, I would suggest removing the minus sign from the computation of the ICS since (-2)*(-1)*fit$value = 2*fit$value = 2*LLH(as defined above, i.e. maximised log likelihood). I think the ICS should be computed from the maximised value of the (log) likelihood function (and not from minimised negative (log) likelihood). Tsay (2002) in Analysis of Financial Time Series states that, in AIC calculation, "the likelihood function is evaluated at the maximum likelihood estimates".
>
> Best regards,
>
> Michal Miklovic
>
>
>
>
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-- 
Yohan Chalabi