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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
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)