Abstract
This study proposes new generalized spectral tests for multivariate martingale difference hypotheses, specifically geared towards 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 US stock market illustrates the usefulness of our proposal.
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