Generalized Spectral Tests for Multivariate Martingale Difference Hypotheses
Wang, Xuexin
JOURNAL OF BUSINESS & ECONOMIC STATISTICS Year: 2024 Volume: 42.0
DOI: 10.1080/07350015.2024.2301954
Abstract: This study proposes new generalized spectral tests for multivariate martingale difference hypotheses, specifically geared toward high-dimensionality scenarios where the dimension of the time series is comparable or even larger than the sample size in practice. We develop an asymptotic theory and a valid wild bootstrapping procedure for the new test statistics, in which the dimension of the time series is fixed. We demonstrate that a bias-reduced version of the test statistics effectively addresses the high-dimensionality concerns. Comprehensive Monte Carlo simulations reveal that the bias-reduced statistic performs substantially better than its competitors. The application to testing the efficient market hypothesis on the U.S. stock market illustrates the usefulness of our proposal.
