    # RE: st: R-squared with ARIMA

 From "Nick Cox" To 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

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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```