🤖 AI Summary
This study addresses the severe inferential bias in conventional predictive ability tests when forecast errors exhibit heavy-tailed distributions—particularly those with infinite variance—where the actual rejection rate at the nominal 5% significance level can surge to as high as 70%. To tackle this issue, the authors establish a new stable limit theorem tailored for strongly mixing time series with infinite variance and propose a subsampling inference method that circumvents the need to estimate either the long-run variance or the tail index, thereby accommodating data with arbitrary tail thickness. The resulting framework delivers robust predictive accuracy testing under heavy-tailedness, substantially correcting the over-rejection problem of traditional tests in emerging market exchange rate risk forecasting and leading to materially revised conclusions about model predictive performance.
📝 Abstract
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.