st: R-squared with ARIMA

[Kit Baum <baum@bc.edu>]

Danielle said

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?




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.


Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html


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