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Re: st: Problem with ARIMA-ARCH model


From   "vasja sivec" <vasja.sivec@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Problem with ARIMA-ARCH model
Date   Mon, 18 Aug 2008 23:51:34 +0200

Dear Statalisters,

Issue resolved. This is an update of why the coefficients in the mean
model when using -arima- command and joint -arch arima- command
differ. Following are the citations from Mr. Brian P. Poi`s (1 and 2)
and Robert A. Yaffee`s (3) email that clarify the issue.

Mr. Poi and Mr. Yaffee thank you for your help.

There are at least three reasons:

1. "By default -arima- uses the unconditional likelihood function for
the ARIMA model, while -arch- uses a conditional likelihood function.
The difference between the two lies in how the first few observations
are handled. For large data sets, the two approaches produce similar
results.  For smaller data sets, the choice does have a noticeable
impact on the coefficients".

2. "Arch with arima command estimates all the parameters jointly. But,
if you first model the conditional mean, obtain the residuals and then
model the with an ARCH process, the coefficients and standard errors
reported by an -arch- do not reflect the fact that the residuals
themselves are estimated and hence subject to sampling variation.  On
the other hand, modeling both processes jointly using -arch-obviates
this issue".

3. "Sometimes when the variance model is more properly specified, the
mean model parameter estimates emerge as similar although not
identical. This is a common problems with nonlinear models such as the
GARCH type. You might try other specifications of your GARCH model".

Other specifications did produce better results.

Kind regards,
Vasja Sivec
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