The mean squared prediction error paradox

In this paper, we show that traditional comparisons of mean squared prediction error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as “the MSPE paradox.” We characterize “paradox zones” in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non-empty sets. Finally, we illustrate the relevance of the paradox with a few empirical applications.