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Testing for high-dimensional white noise using maximum cross-correlations

Author

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  • Jinyuan Chang
  • Qiwei Yao
  • Wen Zhou

Abstract

SUMMARY We propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the $L_\infty$-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods, including the Lagrange multiplier test and the multivariate Box–Pierce portmanteau tests, especially when the dimension of the time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre-transformed data obtained via the time series principal component analysis proposed by J. Chang, B. Guo and Q. Yao (arXiv:1410.2323). The proposed procedures have been implemented in an R package.

Suggested Citation

  • Jinyuan Chang & Qiwei Yao & Wen Zhou, 2017. "Testing for high-dimensional white noise using maximum cross-correlations," Biometrika, Biometrika Trust, vol. 104(1), pages 111-127.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:111-127.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw066
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    Citations

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    Cited by:

    1. Loubaton, Philippe & Rosuel, Alexis & Vallet, Pascal, 2023. "On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Xiandeng Jiang & Le Chang & Yanlin Shi, 2023. "Housing price diffusions in mainland China: evidence from a spatially penalized graphical VAR model," Empirical Economics, Springer, vol. 64(2), pages 765-795, February.
    3. Gao, Zhaoxing & Tsay, Ruey S., 2023. "A Two-Way Transformed Factor Model for Matrix-Variate Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 83-101.
    4. He, Yong & Zhang, Mingjuan & Zhang, Xinsheng & Zhou, Wang, 2020. "High-dimensional two-sample mean vectors test and support recovery with factor adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    5. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2022. "Data-driven portmanteau tests for time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 675-698, September.
    6. Li, Shuangbo & Zhang, Li-Xin, 2019. "Identifying the number of factors using a white noise test," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 92-99.
    7. Li, Muyi & Zhang, Yanfen, 2022. "Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    8. Xuexin WANG, 2021. "Generalized Spectral Tests for High Dimensional Multivariate Martingale Difference Hypotheses," Working Papers 2021-11-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    9. Gao, Zhaoxing & Tsay, Ruey S., 2021. "Modeling high-dimensional unit-root time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1535-1555.
    10. Zhaoxing Gao & Ruey S. Tsay, 2020. "Modeling High-Dimensional Unit-Root Time Series," Papers 2005.03496, arXiv.org, revised Aug 2020.
    11. Zhaoxing Gao & Ruey S. Tsay, 2020. "A Two-Way Transformed Factor Model for Matrix-Variate Time Series," Papers 2011.09029, arXiv.org.
    12. Tsay, Ruey S., 2020. "Testing serial correlations in high-dimensional time series via extreme value theory," Journal of Econometrics, Elsevier, vol. 216(1), pages 106-117.
    13. Chang, Jinyuan & Jiang, Qing & Shao, Xiaofeng, 2023. "Testing the martingale difference hypothesis in high dimension," Journal of Econometrics, Elsevier, vol. 235(2), pages 972-1000.
    14. Baek, Changryong & Gates, Katheleen M. & Leinwand, Benjamin & Pipiras, Vladas, 2021. "Two sample tests for high-dimensional autocovariances," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

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