Re: st: Problem with ARIMA-ARCH model

 From Robert A Yaffee To statalist@hsphsun2.harvard.edu Subject Re: st: Problem with ARIMA-ARCH model Date Mon, 18 Aug 2008 10:16:49 -0400

```Dear Vasja,
The variance model is not robust to misspecification of the mean model.
You need to properly specify your mean model before attempting to
model the conditional error variance.    Variations in specification of the mean
model will clearly affect the modeling of the conditional error variance from it.
Regards,
Bob Yaffee

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2008.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: vasja sivec <vasja.sivec@gmail.com>
Date: Monday, August 18, 2008 10:03 am
Subject: st: Problem with ARIMA-ARCH model
To: statalist@hsphsun2.harvard.edu

> 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|
> ar
> L1.            -.8310875            0.000
> ma
> L1.             .811545              0.000
>
> . arch dlndax, arch(1) arima(1,0,1) noconstant nolog
>
> ARMA        Coef.                  P>|z|
> ar
> L1.           .2875023              0.079
> ma
> L1.           -.2352394             0.167
>
> ARCH        Coef.                   P>|z|
> arch
> 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
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```