A Frequency-Domain Test for Multivariate White Noise

In this paper, we propose a novel frequency-domain test for multivariate time series white noise. The proposed test statistic is constructed by maximizing two normalized cumulative sums of frequency-domain series. Under the null hypothesis, each normalized cumulative sum converges in distribution to a standard Brownian bridge. The numerical results indicate that the proposed statistic outperforms commonly-used-ones both in empirical size and in empirical power. Not only the proposed test is independent of any choice of lag parameter, but the computation is very efficient with the aid of the function qCvM in R package goftest.