Tests for white noise via asymptotically independent U-statistics in high-dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918486166470656 |
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| author | Xu, Yuanya |
| author_facet | Xu, Yuanya |
| contents | We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the null, asymptotic normality is established as $p, T \to \infty$ jointly using martingale difference theory. Our approach imposes no cross-sectional independence assumption, requiring only spectral conditions on $Σ_0$. Theoretically, we link cross-sectional correlations to a graph structure, integrating algebraic and geometric analyses to facilitate the derivation. Simulations confirm reliable size control and satisfactory power across various $(p, T)$ settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04968 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tests for white noise via asymptotically independent U-statistics in high-dimensions Xu, Yuanya Methodology Statistics Theory We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the null, asymptotic normality is established as $p, T \to \infty$ jointly using martingale difference theory. Our approach imposes no cross-sectional independence assumption, requiring only spectral conditions on $Σ_0$. Theoretically, we link cross-sectional correlations to a graph structure, integrating algebraic and geometric analyses to facilitate the derivation. Simulations confirm reliable size control and satisfactory power across various $(p, T)$ settings. |
| title | Tests for white noise via asymptotically independent U-statistics in high-dimensions |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2605.04968 |