R help - Feb 2003 - GARCH with t-innovations

Dear all,

Can garch function fit also t-innovations or only Gaussian innovations?

-- 
With kind regards -- Lepo pozdravljeni -- Gr??e (Gr?ezi) --

					       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

> Can garch function fit also t-innovations or only Gaussian innovations?
The latter -- Adrian's code uses analytic gradients, and those are always
tied to the particular distribution of innovations for which they were 
derived.  You could of course do the legwork of coding this for the t-dist, 
IIRC an old Bollerslev paper has all/most of the math, release it as a 
(GPL'ed) patch and thereby secure your claim to fame as another co-author
of tseries.

Dirk 
(who has a more modest patch in tseries)

-- 
According to the latest figures, 43% of all signatures are totally worthless.

> 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 -- Gr??e (Gr?ezi) --
>
>                                                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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