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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?

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  • $\begingroup$ Why don't you do 1-day ahead predictions by re-estimating the model daily vs the fixed parameter model predictions. Then you can do Diebold-Mariano. Make sure too keep a constant window length for your daily re-estimations. $\endgroup$ – stollenm Apr 19 '18 at 6:09
  • $\begingroup$ Daniel, see my answers here and here. They were written for different questions but might be somewhat relevant to this one, too. $\endgroup$ – Richard Hardy Apr 20 '18 at 16:21
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In sample, you would look at goodness-of-fit measures, such as Bayes Information Criterion (BIC), Akaike Information Criterion (AIC) or R^2.

Generally speaking, the more parameters your model has, the better you can fit the data. For this reason there it is difficult to define a "fair" way to compare in sample fit. BIC and AIC have penalty terms for the number of parameters but theses are chosen somewhat heuristically.

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  • $\begingroup$ Thanks @stollenm. I think I should have explained the issue better I just added a small paragraph above. $\endgroup$ – Daniel Pinto Apr 18 '18 at 12:47

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