I would hazard the guess that this would be better estimated as a multivariate time series (e.g. AR1) in which the covariance between the two innovation components was NOT assumed to be 0 (nor were their variances assumed to be the same). The R time series task view lists packages to do this, but ?ar might be a place to start.
I would happily defer to expert opinion on this matter, however. I just always get this funny rumbling in my stomach whenever anyone proposes simple lagged regression models for time series. Maybe it's the burrito, though... -- Bert On Tue, Aug 31, 2010 at 8:53 AM, Duncan Murdoch <[email protected]>wrote: > On 31/08/2010 11:00 AM, David Winsemius wrote: > >> On Aug 31, 2010, at 10:35 AM, <[email protected]> < >> [email protected] > wrote: >> >> > Hi Duncan, >> > >> > Thanks for your response. >> > >> > Indeed, independent normal errors were what I had in mind. As for > >> variances, if I assume they are the same, would a 'pooled model' > apply in >> this case? Is that equivalent to your suggestion of > concatenating x(1,t) >> and x(2,t)? >> > >> >> Wouldn't this be equivalent to a segmented regression analysis that would >> estimate the slopes in the two periods as mu(1) and mu(2), throw- away any >> level shift estimate at the join-point, and which then estimated the >> residual one-lag autocorrelation (again omitting the join point) and >> assigned that value to "d"? >> >> >> > > That is a different model. In the given situation, successive observations > are correlated, so if x(1, t) had a large residual above the line, x(1, t+1) > would be expected to have a large residual as well, and as long as |d-1| is > less than 1, the given model would have zero slope in the long run. > > > Duncan Murdoch > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html> > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
