[R] Re: GARCH with t-innovations

[Adrian Trapletti]

> Subject: [R] GARCH with t-innovations
> Date: 21 Feb 2003 14:07:44 +0100
> From: Gorazd Brumen <gbrumen at student.ethz.ch>
> To: r-help at stat.math.ethz.ch
>
> Dear all,
>
> Can garch function fit also t-innovations or only Gaussian innovations?
>
> --
> With kind regards -- Lepo pozdravljeni -- Grüße (Grüezi) --
>
>                                                Gorazd Brumen
> -------------------------------
> Mail 1: gbrumen at student.ethz.ch
> Mail 2: gorazd.brumen at fmf.uni-lj.si
> Tel.: +41 (0)1 63 34906
> Homepage: valjhun.fmf.uni-lj.si/~brumen

The estimator provided by the garch function is the maximum likelihood estimator under conditional normality. Under conditional-nonnormality (e.g., t-distribution) the estimator is a quasi-maximum likelihood
estimator which is still consistent under certain (more restrictive than Gaussian case) assumptions. However, the standard errors as computed by the garch function are in the latter case not any more consistent.

For an overview see section 8 of the first citation in the help page of the garch function.

For practical purposes, that means you can fit a garch model with the garch function, take the residuals and fit, e.g., a t-distribution. This might be a consistent estimation procedure, however unless the residuals
are Gaussian not the ideal one.

best
Adrian

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