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PreprintarXiv licencearXiv

An adaptive L2-type test for high-dimensional white noise

  • Jinyuan Chang
  • Jing He
  • Weiming Li
  • Chen Lin
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Abstract

We propose a new L2-type test for white noise which allows the dimension p of the time series to either (i) be a fixed constant, or (ii) diverge with the sample size n. The proposed test statistic exhibits an interesting phase transition, following two different regimes of behavior: p is fixed, and p→∞. Because identification of the operable regime is difficult, if not impossible in practice, we devise a novel adaptive bootstrap method to construct unified testing procedure across different phases. Numerical experiments confirm the good finite sample performance of the proposed adaptive L2-type test in comparison to the existing methods in the literature. The proposed testing procedure has been implemented in R package HDTSA.

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Cite

BibTeXRIS
BibTeX
@misc{chang2026adaptive,
  title = {{An adaptive $L_2$-type test for high-dimensional white noise}},
  author = {Jinyuan Chang and Jing He and Weiming Li and Chen Lin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.33418},
  eprint = {2609.33418},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.33418},
}
RIS
TY  - UNPB
TI  - An adaptive L_2-type test for high-dimensional white noise
AU  - Jinyuan Chang
AU  - Jing He
AU  - Weiming Li
AU  - Chen Lin
PY  - 2026
DA  - 2026/09/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.33418
UR  - https://arxiv.org/abs/2609.33418
AB  - We propose a new L_2-type test for white noise which allows the dimension p of the time series to either (i) be a fixed constant, or (ii) diverge with the sample size n. The proposed test statistic exhibits an interesting phase transition, following two different regimes of behavior: p is fixed, and p→∞. Because identification of the operable regime is difficult, if not impossible in practice, we devise a novel adaptive bootstrap method to construct unified testing procedure across different phases. Numerical experiments confirm the good finite sample performance of the proposed adaptive L_2-type test in comparison to the existing methods in the literature. The proposed testing procedure has been implemented in R package HDTSA.
ER  -