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st: Problem with ARIMA-ARCH model

From   "vasja sivec" <>
Subject   st: Problem with ARIMA-ARCH model
Date   Mon, 18 Aug 2008 16:02:05 +0200

Dear Statalist users,

I have a DAX stock index return series and I am trying to model its
volatility with ARCH type model. First I modeled the return series
itself to obtain the residuals which enter into the ARCH model. The
most appropriate model for returns was ARIMA (1,0,1) model with no
constant. Then I estimated an ARCH(1) model with the residuals
obtained from ARIMA model. But now, the coefficients of ARIMA model
have completely changed. This is what happened:

. arima dlndax, arima(1,0,1) noconstant nolog

ARMA        Coef.                  P>|z|
L1.            -.8310875            0.000
L1.             .811545              0.000

. arch dlndax, arch(1) arima(1,0,1) noconstant nolog

ARMA        Coef.                  P>|z|
L1.           .2875023              0.079
L1.           -.2352394             0.167

ARCH        Coef.                   P>|z|
L1.           .3028063              0.000
_const.     .0001436              0.000

How come that ARCH estimation affects the ARIMA model? Isn`t this a
one-way road (ex.: ARIMA->get residuals->calculate cond.
variances->estimate ARCH->the end)?

Thank you for any kind of help,
Vasja Sivec
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