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

Chang, Jinyuan, Yao, Qiwei ORCID: 0000-0003-2065-8486 and Zhou, Wen (2017) Testing for high-dimensional white noise using maximum cross-correlations. Biometrika, 104 (1). 111 - 127. ISSN 0006-3444

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Identification Number: 10.1093/biomet/asw066


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∞-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.

Item Type: Article
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Additional Information: © 2017 Biometrika Trust
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
JEL classification: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General
Date Deposited: 06 Dec 2016 14:01
Last Modified: 20 Oct 2021 00:24
Funders: Central Universities of China, National Natural Science Foundation of China, Center of Statistical Research at Southwestern University of Finance and Economics, U.K. Engineering and Physical Sciences Research Council, U.S. National Science Foundation

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