[R] simultaneous estimation

[Duncan Murdoch]

On 31/08/2010 11:00 AM, David Winsemius wrote:
> On Aug 31, 2010, at 10:35 AM, <Murali.Menon at avivainvestors.com> <Murali.Menon at 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