GLS with AR(k) errors

[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.

[TomDoan]

Use BOXJENK with the GLS option (under "Options for REGARIMA Models").

[ying2728]

If one of the regressors is lagged y, y(t-1), is it still OK? Thanks.

[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.

[ying2728]

How about using MA(k) errors? Same problem?

[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?