Error terms in state space object

[workhard]

According to Eveiews 6 User Guide II page 390, section "error and variances", am i right to say that the error term of a state space equation is expressed by using the variance of the prediction residuals? I just worry that I interpret wrongly the meaning of the manual.

On top of that, page 391 stated that the specified variance may be a known constant value, expression containing unknown parameters to be estimated or build time-variation into the variances using a series expression. In the latter case, is it meaning that we are considering the GARCH (since we allow the variances to be time-varying) ?

Any reply is appreciated..

[EViews Glenn]

I'm not certain what you mean by the variance of the prediction residuals in this context since the equation is defined without reference to the t-1 conditioning set. The prediction residuals have an entirely different variance which depends in part on the equation variance.

As to GARCH comment, you are correct that you can make the variances time-varying by having them depend on an exogenous variable, but the variances cannot be autoregressive nor can they be functions of past residuals so I think you're stretching a bit...

[workhard]

Thanks for your reply.
I think I misinterpret the meaning of the manual.
If you don't mind, can you explain to me the statements below in Eviews 6 User Guide II, page 390?
"In a sspace object, the equation specifications in a signal or state equation do not contain error terms unless specified explicitly. The easiest way to add an error to a state sapce equation is to specify an implied error term using its variance."
Actually I don't really understand what does it mean by "specify an implied error term using its variance". In page 383, equation 35.1, we have yt = ct + Ztαt + εt. So i thought that the error term in the equation is the variance of εt. Also, in what situation we should specified the error term?

Regarding the 2nd issue, seems like this is not the right way to deal with heteroscedasticity. Any suggestion how can I consider heteroscedasticity in state space models?

Thanks!!

[EViews Glenn]

I'm not certain that I understand the question. Some state and signal equations do not have error terms. In those cases, you need not add an error specification. For example, state equations which describe the lags of a state do not have error terms. In other cases there is an explict error which must be specified.

In your example, specifying the variance of an equation does specify the variance of the error term. That's what we mean by an implied error. When you specify a variance you are saying that the equation has an error, and that the error has a variance given by the specification.

You can add deterministic heteroskedasticity by using an expression for the variance, but I don't believe there is an easy way to specify the dynamics for a GARCH error structure.