Diebold-Mariano test in case of nested models (Clark & McCracken, 2001) I have become aware of Clark & McCracken (2001) showing that the asymptotics of the Diebold-Mariano test will potentially collapse when comparing forecast accuracy of nested models (such as GARCH / GJR-GARCH / APARCH). 
How badly will this affect my results?
References:


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*Clark, Todd E., and Michael W. McCracken. "Tests of equal forecast accuracy and encompassing for nested models." Journal of Econometrics 105.1 (2001): 85-110.

 A: It depends on what you want to learn from the test result.


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*If you wonder whether one forecast (say, $f_1$) is statistically more accurate than another (say, $f_2$), the Diebold-Mariano (DM) test will tell you that. At this point there is no talk of the models that generated the forecasts.
The DM test (as any other statistical test) targets making inference on the population rather than the current sample. If (1) the DM test tells you with 95% confidence that $f_1$ beats $f_2$ and (2) the forecast generating processes and the data generating process all remain unchanged in the future, then you would expect that $f_1$ will beat $f_2$ also in the future.
How can you benefit from this result? If you have the forecast generating process available, you could choose to use the one for $f_1$ rather than for $f_2$. However, Diebold (2015) does not encourage that:

The Diebold-Mariano (DM) test was intended for comparing forecasts; it has
  been, and remains, useful in that regard. The DM test was not intended for comparing models. Much of the large ensuing literature, however, uses DM-type tests for comparing models, in pseudo-out-of-sample environments. In that case, simpler yet more compelling full-sample model comparison procedures exist; they have been, and should continue to be, widely used.


*If you wonder which of the alternative models is more likely to have generated the data, using the DM test will be problematic in case of nested models, as explained in Clark & McCracken (2001). (Once again, Diebold did not intend the test to be used for comparing models -- see the quote above.)
How bad does the DM fail in this sense? There are simulation results reported in the tables of Clark & McCracken (2001), you may check them.
References:


*

*Clark, Todd E., and Michael W. McCracken. "Tests of equal forecast accuracy and encompassing for nested models." Journal of Econometrics 105.1 (2001): 85-110.
Free version here.

*Diebold, Francis X. "Comparing predictive accuracy, twenty years later: A personal perspective on the use and abuse of Diebold–Mariano tests." Journal of Business & Economic Statistics 33.1 (2015): 1-9.
Free version here.

