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.

中文翻译：

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均方预测误差悖论

在本文中，我们表明，两种竞争预测之间的均方预测误差（MSPE）的传统比较可能存在很大争议。之所以如此，是因为当不满足某些特定的效率条件时，显示最低 MSPE 的预测也将显示与目标变量的最低相关性。鉴于预测文献中违反效率的情况很常见，因此在准确性和与目标变量的相关性方面的这种相反行为可能是一个相当常见的经验发现，我们在此将其标记为“MSPE 悖论”。我们根据与目标变量相关性的差异来描述“悖论区域”，并进行一些简单的模拟来表明这些区域可能是非空集。最后，我们通过一些实证应用来说明该悖论的相关性。