We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of the time. To establish these results, we develop a new stable limit theorem for strongly mixing, infinite-variance time series processes. Building on this theory, we consider sub-sampling-based inference that remains valid irrespective of tail-heaviness and requires no estimation of long-run variances or tail indices. An application to risk forecasts for emerging-market exchange rates shows that accounting for heavy tails can substantially alter conclusions about predictive performance relative to standard procedures.

翻译：本文研究当预测误差呈现重尾特征时，用于评估和比较预测精度的常用检验方法的渐近行为。具体而言，当损失差分序列具有无限方差时，Diebold-Mariano检验统计量收敛于包含非高斯稳定随机变量的非标准极限分布。因此，传统临界值会导致严重扭曲的推断：名义显著性水平为5%的检验拒绝真实原假设的频率可能高达70%。为建立这些结论，我们提出了适用于强混合无限方差时间序列过程的新型稳定极限定理。基于该理论，我们发展了无需估计长期方差或尾部指数的子抽样推断方法，该方法对任意重尾程度均保持有效性。将所提方法应用于新兴市场汇率风险预测的实证研究表明，与标准程序相比，考虑重尾特征会显著改变关于预测绩效的结论。