Pith Number

pith:23V3ROKV

pith:2026:23V3ROKVWZMID2D3N5FMUG5GD6

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Heavy Tails and Predictive Ability Testing

Jonas F. Frederikse, Muneya Matsui, Rasmus S. Pedersen

When loss differentials have infinite variance the Diebold-Mariano test statistic converges to a non-Gaussian stable limit instead of a normal distribution.

arxiv:2605.16866 v1 · 2026-05-16 · stat.ME · econ.EM

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

107 extracted · 107 resolved · 1 Pith anchors

[1] 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 2016

[2] 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 2022

[3] 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 2011

[4] Basrak, B. and J. Segers (2009): Regularly varying multivariate time series, Stochastic Processes and their Applications, 119, 1055--1080 2009

[5] Buraczewski, D., E. Damek, and T. Mikosch (2016): Stochastic Models with Power-Law Tails: The Equation X=AX+B , Switzerland: Springer 2016

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:27.193397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6ebb8b955b65881e87b6f4aca1ba61fbee78c3ec9ffc3d0024e2f5406b43dc8

Aliases

arxiv: 2605.16866 · arxiv_version: 2605.16866v1 · doi: 10.48550/arxiv.2605.16866 · pith_short_12: 23V3ROKVWZMI · pith_short_16: 23V3ROKVWZMID2D3 · pith_short_8: 23V3ROKV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/23V3ROKVWZMID2D3N5FMUG5GD6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d6ebb8b955b65881e87b6f4aca1ba61fbee78c3ec9ffc3d0024e2f5406b43dc8

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
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