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It is well-known that the weighted averages of two competing forecasts may reduce mean squared prediction errors (MSPE) and may also introduce certain inefficiencies. In this paper, we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes: Mincer and Zarnowitz inefficiency or auto-inefficiency for short. Under mild assumptions, we show that linear convex forecast combinations are almost always auto-inefficient, and, therefore, greater reductions in MSPE are almost always possible. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when individual forecasts are efficient. Furthermore, we show that the so-called "optimal weighted average" traditionally presented in the literature may indeed be inefficient as well. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of headline inflation forecasts for eight European economies. Overall, our results indicate that in situations in which a number of different forecasts are available, the combination of all of them should not be the last step taken in the search of forecast accuracy. Attempts to take advantage of potential inefficiencies stemming from the combination process should also be considered. [ABSTRACT FROM AUTHOR]

In this paper, we present a new asymptotically normal test for out-of-sample evaluation in nested models. Our approach is a simple modification of a traditional encompassing test that is commonly known as Clark and West test (CW). The key point of our strategy is to introduce an independent random variable that prevents the traditional CW test from becoming degenerate under the null hypothesis of equal predictive ability. Using the approach developed by West (1996), we show that in our test, the impact of parameter estimation uncertainty vanishes asymptotically. Using a variety of Monte Carlo simulations in iterated multi-step-ahead forecasts, we evaluated our test and CW in terms of size and power. These simulations reveal that our approach is reasonably well-sized, even at long horizons when CW may present severe size distortions. In terms of power, results were mixed but CW has an edge over our approach. Finally, we illustrate the use of our test with an empirical application in the context of the commodity currencies literature. [ABSTRACT FROM AUTHOR]