On Aug 31, 2010, at 10:35 AM, <murali.me...@avivainvestors.com> <murali.me...@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"?
--
David.
Cheers,
Murali
-----Original Message-----
From: Duncan Murdoch [mailto:murdoch.dun...@gmail.com]
Sent: 31 August 2010 12:31
To: Menon Murali
Cc: r-help@r-project.org
Subject: Re: [R] simultaneous estimation
On 31/08/2010 6:58 AM, murali.me...@avivainvestors.com wrote:
Hi folks,
Not sure what this sort of estimation is called. I have a 2-column
time-series x(i,t) [with (i=1,2; t=1,...T)], and I want to do the
following 'simultaneous' regressions:
x(1,t) = (d - 1)(x(1, t-1) - mu(1))
x(2,t) = (d - 1)(x(2, t-1) - mu(2))
And I want to determine the coefficients d, mu(1), mu(2).
Note that the d should be the same for both estimations, whereas
the coefficients mu will have two values mu(1), mu(2), one for each
estimation.
Is this possible to do in R?
What would be the corresponding syntax in, say, lm?
Your specification is not complete: you haven't said what the errors
will be, or how x(1,1) and x(2,1) are determined. I assume you mean
independent normal errors, but are you willing to assume the
variance is the same in both series? If so, then your model is
almost equivalent to a linear model with concatenated x(1,t) and
x(2,t) values. (This would be the "partial likelihood" version of
the model, where you don't try to fit x(i, 1), but you fit the rest
of the values conditional on earlier
ones.)
If you want the full likelihood or you want separate variances for
the two series, you probably need to write out the likelihood
explicitly and maximize it.
Duncan Murdoch
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