Jonas F. Frederiksen, Muneya Matsui, Rasmus S. Pedersen
arXiv 16 May 2026 · Statistics — Methodology
arXiv:2605.16866 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 43% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kim, J., N. Meddahi, and M. Yamashita (2021) Forecast comparison tests under fat-tails, Working paper accessed on 24 November 2025 via https://www.ecb.europa.eu/press/confer… | 1.000 | 5 | 3 | 100% |
| 2 | Davis, R. A. and T. Hsing (1995) Point process and partial sum convergence for weakly dependent random variables with infinite variance | 0.928 | 4 | 3 | 100% |
| 3 | Politis, D. N., J. P. Romano, and M. Wolf (1999) Subsampling | 0.894 | 7 | 3 | 71% |
| 4 | Hansen, P. R (2005) A test for superior predictive ability | 0.888 | 10 | 3 | 70% |
| 5 | Kokoszka, P. and M. Wolf (2004) Subsampling the mean of heavy-tailed dependent observations | 0.874 | 6 | 2 | 100% |
| 6 | Diebold, F. X. and R. S. Mariano (1995) Comparing predictive accuracy | 0.874 | 5 | 2 | 100% |
| 7 | Ibragimov, I. A (1962) Some limit theorems for stationary processes | 0.874 | 5 | 2 | 100% |
| 8 | White, H (2000) A reality check for data snooping | 0.811 | 4 | 2 | 100% |
| 9 | Matsui, M., T. Mikosch, and O. Wintenberger (2025) b): Self-normalized partial sums of heavy-tailed time series self | 0.754 | 7 | 3 | 43% |
| 10 | McElroy, T. and D. N. Politis (2002) Robust inference for the mean in the presence of serial correlation and heavy-tailed distributions | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 45 scored citations.