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RE: st: R-squared with ARIMA


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: R-squared with ARIMA
Date   Thu, 15 Jun 2006 22:35:58 +0100

I am not totally clear what lies behind this question. 

R^2 _is_ in essence a squared correlation. That is 
presumably why the notation is as it is. 

This is easiest to see with a bivariate regression. 
The correlation between y and x is the same as 
the correlation between y and predicted y, 
say a + bx. 

The square of the correlation is equal to R^2
as given in regression results. 

This is covered in most if not all texts on regression. 

The approach Kit is taking is to focus on 
the correlation between y and predicted y as 
something that can generally be calculated, 
way beyond bivariate regression, 
and squared to produce a measure that varies 
between 0 and 1. In practice the correlation
will already be positive, but for comparability 
-- and for the interpretation you want -- 
squaring is essential. 

That idea is already discussed in the FAQ which
answers your question: 

FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself R-squared
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        9/03    How can I get an R-squared value when a Stata command
                does not supply one?
                http://www.stata.com/support/faqs/stat/rsquared.html

Whether you want to call the measure R-squared or an analogue of that
is largely a matter of taste. But you can calculate this measure regardless
of howr the predicted values are produced. 

Incidentally, I am not clear that ARIMA is intrinsically econometric. 
The present form of ARIMA owes most to Box and Jenkins, neither of
them economists or econometricians. 

Nick 
n.j.cox@durham.ac.uk 

Danielle H. Ferry
 
> Thanks, Kit. But why do you square the correlation?

Kit Baum 
 
> > A measure of R^2 that does not depend on the method of computation 
> > is  the squared correlation between observed and in-sample 
> forecast  
> > values. Indeed, the forecast values could come from a subjective 
> >  process or a crystal ball. But if you can generate in-sample  
> > forecasts from your models, you can always compute this measure.

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