Heavy Tails and Predictive Ability Testing

Fuente: arXiv
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Autori principali: Frederiksen, Jonas F., Matsui, Muneya, Pedersen, Rasmus S.
Natura: Preprint
Pubblicazione: 2026
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author Frederiksen, Jonas F.
Matsui, Muneya
Pedersen, Rasmus S.
author_facet Frederiksen, Jonas F.
Matsui, Muneya
Pedersen, Rasmus S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_16866
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Heavy Tails and Predictive Ability Testing
Frederiksen, Jonas F.
Matsui, Muneya
Pedersen, Rasmus S.
Methodology
Econometrics
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.
title Heavy Tails and Predictive Ability Testing
topic Methodology
Econometrics
url https://arxiv.org/abs/2605.16866