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 <murdoch.duncan@gmail.com>wrote:

> On 31/08/2010 11:00 AM, David Winsemius wrote:
>
>> On Aug 31, 2010, at 10:35 AM, <Murali.Menon@avivainvestors.com> <
>> Murali.Menon@avivainvestors.com  > 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
>
> ______________________________________________
> R-help@r-project.org 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]]

