Testing for high-dimensional white noise using maximum cross correlations
Qiwei Yao and
LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library
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[infinity]-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 the 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, for example, the Lagrange multiplier test and the multivariate Box–Pierce portmanteau tests, especially when the dimension of 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 Chang, Guo and Yao (arXiv:1410.2323). The proposed procedures have been implemented in an 'R' package.
Keywords: autocorrelation; normal approximation; parametric bootstrap; portmanteau test; time series principal component analysis; vector white noise (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
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Published in Biometrika, 18, February, 2017, 104(1), pp. 111-127. ISSN: 0006-3444
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