Generalized Spectral Tests for Multivariate Martingale Difference Hypotheses
针对高维时间序列数据（维度接近或超过样本量），提出新的广义谱检验方法，通过偏差修正和自助法提升检验效率，在模拟和美股市场有效性检验中表现优于现有方法。
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.