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GLS with AR(k) errors
Posted: Fri Aug 21, 2015 1:03 am
by ying2728
I want to estimate a linear equation by GLS with AR(k) errors:
y(t) = a + b x(t) + e(t),
where e(t) is an AR(k) series
Are there program codes available? Thanks.
Re: GLS with AR(k) errors
Posted: Fri Aug 21, 2015 8:11 am
by TomDoan
Use
BOXJENK with the GLS option (under "Options for REGARIMA Models").
Re: GLS with AR(k) errors
Posted: Sat Aug 22, 2015 3:48 am
by ying2728
If one of the regressors is lagged y, y(t-1), is it still OK? Thanks.
Re: GLS with AR(k) errors
Posted: Sat Aug 22, 2015 7:32 am
by TomDoan
No. You can't freely estimate a model like that. That's actually saying that Y is an AR(4) which means that there are four different identically fitting ways to write it as an AR(1) with AR(3) errors.
Re: GLS with AR(k) errors
Posted: Sat Aug 22, 2015 8:21 pm
by ying2728
How about using MA(k) errors? Same problem?
Re: GLS with AR(k) errors
Posted: Sat Aug 22, 2015 8:45 pm
by TomDoan
Potentially different problem with cancellation if the error process isn't anywhere near that complicated. Is there a reason that you're not just fitting a minimal ARMA model?