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
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