Testing serial correlations in high-dimensional time series via extreme value theory

This paper proposes a simple test for detecting serial correlations in high-dimensional time series. The proposed test makes use of the robust properties of Spearman’s rank correlation and the theory of extreme values. Asymptotic properties of the test statistics are derived under some minor conditions as both the sample size and dimension go to infinity. The test is not sensitive to the underlying distribution of the time series so long as the data are continuously distributed. In particular, the existence of finite-order moments of the underlying distribution is not required, and asymptotic critical values of the test statistics are available in closed form. In finite samples, we correct biases of the sample autocorrelations and conduct simulations to study the performance of the proposed test statistics. Simulation results show that the proposed test statistics enjoy good properties of size and power in finite samples. We apply the proposed test to a 92-dimensional series of asset returns. Finally, a simple R code is available to obtain finite-sample critical values of the test statistics if needed.