{"paper":{"title":"Heavy Tails and Predictive Ability Testing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"When loss differentials have infinite variance the Diebold-Mariano test statistic converges to a non-Gaussian stable limit instead of a normal distribution.","cross_cats":["econ.EM"],"primary_cat":"stat.ME","authors_text":"Jonas F. Frederikse, Muneya Matsui, Rasmus S. Pedersen","submitted_at":"2026-05-16T07:58:02Z","abstract_excerpt":"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 se"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The time series of loss differentials are strongly mixing infinite-variance processes, which is required for the new stable limit theorem to hold and for the subsampling inference to be valid irrespective of tail heaviness.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"When loss differentials have infinite variance, the Diebold-Mariano statistic converges to a non-Gaussian stable limit, and subsampling yields valid inference for strongly mixing infinite-variance time series without estimating long-run variances or tail indices.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"When loss differentials have infinite variance the Diebold-Mariano test statistic converges to a non-Gaussian stable limit instead of a normal distribution.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0b7056dc082f45358d39962980598aace9367bc85f736ee967a3af87cc43e5d4"},"source":{"id":"2605.16866","kind":"arxiv","version":1},"verdict":{"id":"cdffaa6a-5de5-4cc6-ae96-fd79e4605272","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:21:17.814940Z","strongest_claim":"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.","one_line_summary":"When loss differentials have infinite variance, the Diebold-Mariano statistic converges to a non-Gaussian stable limit, and subsampling yields valid inference for strongly mixing infinite-variance time series without estimating long-run variances or tail indices.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The time series of loss differentials are strongly mixing infinite-variance processes, which is required for the new stable limit theorem to hold and for the subsampling inference to be valid irrespective of tail heaviness.","pith_extraction_headline":"When loss differentials have infinite variance the Diebold-Mariano test statistic converges to a non-Gaussian stable limit instead of a normal distribution."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16866/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:31:44.328613Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.120758Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.301694Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.377649Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"59505acec8866842b8d37c4b9260af31d4f302c8d07f2ff11634b000eba65421"},"references":{"count":107,"sample":[{"doi":"","year":2016,"title":"Bai, S., M. S. Taqqu, and T. Zhang (2016): A unified approach to self-normalized block sampling, Stochastic Processes and their Applications, 126, 2465--2493","work_id":"7dc795cb-add3-43aa-a6ff-bd8da34d186c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Barendse, S. and A. J. Patton (2022): Comparing predictive accuracy in the presence of a loss function shape parameter, Journal of Business & Economic Statistics, 40, 1057--1069","work_id":"37b82641-ec08-458b-aac3-19a11746807a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Bartkiewicz, K., A. Jakubowski, T. Mikosch, and O. Wintenberger (2011): Stable limits for sums of dependent infinite variance random variables, Probability Theory and Related Fields, 150, 337--372","work_id":"66b52755-af57-49a6-9cb0-294a34161bdc","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Basrak, B. and J. 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