arXiv 8 May 2026 · Mathematics — Statistics Theory
arXiv:2605.07404 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process, specifically an adjusted-range normalizer for scalars and a matrix normalizer for vectors, our approach avoids direct estimation of the long-run covariance matrix. Consequently, it eliminates the need for the ad hoc bandwidth, kernel, and lag-truncation choices required by traditional methods. We establish the asymptotic theory for these statistics, deriving pivotal null limiting distributions and proving test consistency. Monte Carlo simulations show that the proposed tests effectively mitigate the finite-sample size distortions associated with traditional heteroskedasticity and autocorrelation consistent (HAC) methods, while retaining strong empirical power against conditional predictability alternatives.
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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 | Shao, Xiaofeng (2010) A Self-Normalized Approach to Confidence Interval Construction in Time Series | 1.000 | 5 | 3 | 100% |
| 2 | Hong, Yongmiao and Linton, Oliver and McCabe, Brendan and Sun, Jiaji… (2024) Kolmogorov-Smirnov type testing for structural breaks: A new adjusted-range based self-normalization approach | 0.928 | 4 | 3 | 100% |
| 3 | Giacomini, Raffaella and White, Halbert (2006) Tests of Conditional Predictive Ability | 0.885 | 13 | 5 | 69% |
| 4 | Diebold, Francis X. and Mariano, Roberto S (1995) Comparing Predictive Accuracy | 0.644 | 2 | 2 | 100% |
| 5 | Li, Haiqi and Zhang, Ni and Zhou, Jin (2025) A new self-normalized forecast comparison test | 0.644 | 2 | 2 | 100% |
| 6 | Herrndorf, Norbert (1985) A functional central limit theorem for strongly mixing sequences of random variables | 0.511 | 2 | 1 | 100% |
| 7 | Herrndorf, Norbert (1984) A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables | 0.511 | 2 | 1 | 100% |
| 8 | Andrews, Donald W. K (1991) Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation | 0.405 | 1 | 1 | 100% |
| 9 | Bierens, Herman J (1990) A consistent conditional moment test of functional form | 0.405 | 1 | 1 | 100% |
| 10 | Davidson, James (1994) Stochastic Limit Theory | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 21 scored citations.