Testing Serial Correlation and ARCH Effect of High-Dimensional Time-Series Data

Shiqing Ling, Ruey S. Tsay and Yaxing Yang

Journal of Business & Economic Statistics, 2021, vol. 39, issue 1, 136-147

Abstract: This article proposes several tests for detecting serial correlation and ARCH effect in high-dimensional data. The dimension of data p=p(n) may go to infinity when the sample size n→∞ . It is shown that the sample autocorrelations and the sample rank autocorrelations (Spearman’s rank correlation) of the L1-norm of data are asymptotically normal. Two portmanteau tests based, respectively, on the norm and its rank are shown to be asymptotically χ2-distributed, and the corresponding weighted portmanteau tests are shown to be asymptotically distributed as a linear combination of independent χ2 random variables. These tests are dimension-free, that is, independent of p, and the norm rank-based portmanteau test and its weighted counterpart can be used for heavy-tailed time series. We further discuss two standardized norm-based tests. Simulation results show that the proposed test statistics have satisfactory sizes and are powerful even for the case of small n and large p. We apply the tests to two real datasets. Supplementary materials for this article are available online.

Date: 2021
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DOI: 10.1080/07350015.2019.1647844

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