In this paper, we propose a correlation‐based test for the evaluation of two competing forecasts. Under the null hypothesis of equal correlations with the target variable, we derive the asymptotic distribution of our test using the Delta method. This null hypothesis is not necessarily equivalent to the null of equal Mean Squared Prediction Errors (MSPE). Specifically, it might be the case that the forecast displaying the lowest MSPE also exhibits the lowest correlation with the target variable: this is known as “The MSPE paradox.” In this sense, our approach should be seen as complementary to traditional tests of equality in MSPE. Monte Carlo simulations indicate that our test has good size and power. Finally, we illustrate the use of our test in an empirical exercise in which we compare two different inflation forecasts for a sample of OECD economies. We find more rejections of the null of equal correlations than rejections of the null of equality in MSPE.

中文翻译：

---

基于相关性的可预测性检验

在本文中，我们提出了一种基于相关性的测试来评估两个相互竞争的预测。在与目标变量等相关的原假设下，我们使用 Delta 方法得出检验的渐近分布。此零假设不一定等同于均方预测误差 (MSPE) 的零假设。具体来说，可能出现的情况是，显示最低 MSPE 的预测也表现出与目标变量的最低相关性：这称为“MSPE 悖论”。从这个意义上说，我们的方法应该被视为对 MSPE 中传统平等测试的补充。蒙特卡罗模拟表明我们的测试具有良好的规模和功效。最后，我们说明了我们的测试在实证练习中的使用，其中我们比较了经合组织经济体样本的两种不同的通胀预测。我们发现，在 MSPE 中，拒绝相等相关性无效的情况多于拒绝相等相关性无效的情况。