Optimizing GARCH likelihoods is notoriously difficult.
I suspect that you will find 'nlminb' to be less than perfect,
though it is relatively good. In particular you are likely
to see different behavior depending on whether or not the
data are in percent.
A reference is Winker and Maringer (2006) "The convergence
of optimization based estimators: Theory and application to a
GARCH-model". Available online.
Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")
stat stat wrote:
>Good day,
>
>Here I was trying to write a code for Garch(1,1)
>. As garch problem is more or less an optimization
>problem I also tried to get the algorithm for "nlminb"
>function. What I saw that if use this function
>'nlminb" I can easyly get the estimate of parameters.
>But any other function is not working. I tried to
>write my own code for optimization using Quasi-Newton
>Methods etc but although it is working for ordinary
>non-linear function, it fails in garch case. Therefore
>I am trying to get a step by step documentation for
>nlminb function. I already gone though its help page
>got a look on
>"http://netlib.bell-labs.com/cm/cs/cstr/153.pdf>". But
>it did not solve my problem.
>
>In this regards, can anyone give me any step-by-step
>approach or theory behind the calculation that
>'nlminb" uses? Any help will be highly appreciable.
>
>
>Thanks and regards,
>
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>and provide commented, minimal, self-contained, reproducible code.
>
>
>
>