Hi to all,
I have a question related to the variance of the BEKK(1,1) model which is:
Ht=CC'+Aεt-1ε't-1A'+BHt-1B'
So my question is: what is the treatment of Ht?
In other words how RATS defines (treats) H0 and H1 and so Ht-1 and finaly Ht?
Thank you in advance
Best Regards
Anthony
Treatment of Ht in the variance of BEKK(1,1) model
Re: Treatment of Ht in the variance of BEKK(1,1) model
From the User's Guide (Section 9.3.7 in v9)
Pre-sample Variance
These types of models have a technical issue that needs to be addressed in estimating
them: the variance is generated recursively and the pre-sample values of it are unobservable,
and, unfortunately, the estimates can be somewhat sensitive to the choice
made for these.
For the basic arch model, it’s possible to start the estimation at entry q+1, as the
variance depends only upon the lagged u’s, which are (in general) computable given
the set of parameters. If you wish to do this, use the option CONDITION. However,
that isn’t available for a garch model, because the required lag of h can’t be computed
no matter how many data points are used.
By default, the GARCH instruction handles both the pre-sample lagged squared u’s
and the lagged variances by setting them to the unconditional estimates: the variance
from the least squares estimate of the mean model. If you wish to use a different
value, you can include the option PRESAMPLE=pre-sample variance. Because
of this method of handling the pre-sample information, any arch or garch model
with the same mean model can be estimated over the same range, that is, the only
constraint on the range is from the dependent variable and any regressors or “x”-
regressors.
Pre-sample Variance
These types of models have a technical issue that needs to be addressed in estimating
them: the variance is generated recursively and the pre-sample values of it are unobservable,
and, unfortunately, the estimates can be somewhat sensitive to the choice
made for these.
For the basic arch model, it’s possible to start the estimation at entry q+1, as the
variance depends only upon the lagged u’s, which are (in general) computable given
the set of parameters. If you wish to do this, use the option CONDITION. However,
that isn’t available for a garch model, because the required lag of h can’t be computed
no matter how many data points are used.
By default, the GARCH instruction handles both the pre-sample lagged squared u’s
and the lagged variances by setting them to the unconditional estimates: the variance
from the least squares estimate of the mean model. If you wish to use a different
value, you can include the option PRESAMPLE=pre-sample variance. Because
of this method of handling the pre-sample information, any arch or garch model
with the same mean model can be estimated over the same range, that is, the only
constraint on the range is from the dependent variable and any regressors or “x”-
regressors.