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.