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st: R-squared with ARIMA

From   "Danielle H. Ferry" <>
Subject   st: R-squared with ARIMA
Date   Thu, 15 Jun 2006 11:12:40 -0400

Dear Statalisters,

This is less a Stata question than an econometric one, but perhaps someone out
there will not mind answering anyway...

I am estimating a series of models using -arima- (ar(1) & arma(1,1)). I will
be presenting the results to a group w/ very little, if any, econometric
knowledge, and would like to compute the R-squared, since the interpretation
of BIC is not easy for the general public. 

I know that the R-squared with MLE is not valid for comparing models, but is
it ok to use it as a general measure of goodness of fit of individual models?

Assuming the answer to this is yes... I can easily compute R-squared =
(TSS-RSS)/TSS, where TSS = sum of squares of y-ybar and RSS = sum of squares
of y-yhat. Sometimes this formula is presented as R-squared = RSS/TSS. I know
that these 2 formulas are equivalent w/ OLS. BUT, experimentation has shown me
that they are not equivalent w/ -arima-. Can someone verify this? 

Thank you.

Danielle Ferry

National Bureau of Economic Research <>

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