[R] simultaneous estimation

[Murali.Menon at avivainvestors.com]

Bert,

I expect you are correct, burrito notwithstanding (wasn't Taco Bell, was it? :-) 

The full model adds differences and lags, and incorporates non-zero covariances in the innovations. I only simplified to get an idea of how to implement in R.
 
For anyone interested, I'm looking at the Balvers and Wu (2006): "Momentum and Mean Reversion across National Equity Markets", Journal of Empirical Finance 13, 24-48.
 
Their model is as follows, with x(i, t) = log of stock index value of country i at time t:
 
x(i, t) = (1 - d(i)) * mu(i) + d(i) * x(i, t - 1) + Sum[rho(i, j) * (x(i, t - j) - x(t - j - 1))] + eps(i, t)
 
where Sum is across J periods, the d(i), mu(i) and rho(i, j) are all specific to each country (i), and the error terms eps(i) have some covariance structure.
 
You can see that the mu(i) term is supposed to capture the drift of the random walk component of stock index movement, the rho(i) is a coefficient for the momentum component, and the d(i) represents long temporary swings in the index.
 
But as there's now a large number of parameters to estimate, a simplifying assumption is that d and rho are common to all the countries, while the mu is specific.
 
Thanks,
 
Murali

________________________________

From: Bert Gunter [mailto:gunter.berton at gene.com] 
Sent: 31 August 2010 17:12
To: Duncan Murdoch
Cc: David Winsemius; r-help at r-project.org; Menon Murali
Subject: Re: [R] simultaneous estimation


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 at gmail.com> wrote:


	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
	
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