Suppose I have two in-sample forecasts from two different non-nested models. I want to check which one produces the best forecasts. A common way is Diebold-Mariano, GiacominiWhite, ENC-T test. However, these tests were designed for out-of-sample forecasts. Would they also work in-sample?
So, in my case, I have a time-invariant model and the same model with time-varying coefficients. I want to check whether it is important to account for time-variation in coefficients. Does AIC still work then? I thought of comparing the R2 in both models, 1 minus tge ratio of the sum of the squared residuals in both models. The issue is where to draw the line. Suppose I have unconditional model R2 of 5% and conditional one of 6 or 7% (I am dealing with asset pricing predictive regressions so the R2s are often even smaller than this). How to decide that this improvement of 1 ,2 3% in the R2 is economically significant based on R2, AIC and so on based on in-sample methods?