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Heavy Tails and Predictive Ability Testing
[Submitted on 16 May 2026 (v1), last revised 7 Jun 2026 (this ve · 2026-06-09 · via stat updates on arXiv.org

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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.

Submission history

From: Muneya Matsui [view email]
[v1] Sat, 16 May 2026 07:58:02 UTC (619 KB)
[v2] Tue, 19 May 2026 09:44:50 UTC (619 KB)
[v3] Sun, 7 Jun 2026 13:11:45 UTC (608 KB)