Using rolling estimates for further analysis

[Gilbril]

Dear all,

I have the following general question which I will briefly summarize:

We would like to test a theory which links out of sample predictability to

1) nonstationarity of the underlying regressors

2) In sample performance of the underlying models

Now here is my question: We have performed rolling regressions and recursive unit root tests. So we achieve

1) A time varying Theils-U

2) A time varying R2

3) Test statisic / p-values of the underlying models

Is there any reason why 1 cannot be regressed on/compared to 2+3? Recursive and rolling regressions are originally designed to determine stability of coefficients or models so we are unsure whether they should be used in a second step.( Its obvious that the series will be higly autocorrelated so this problem has to be dealt with.)

Any comments or suggestions are higly appreciated

Best Regards
Gilbril

[IRJ]

I don't see what you would gain from regressing Theil's U on an R squared and p-values. I know of no test statistic that does that. Perhaps it would be interesting to plot (or compare across models) the rolling Theil's U, the rolling R squared and the rolling p-values.