| Content | This study proposes new generalized spectral tests for multivariate Martingale Difference
Hypotheses, especially suitable for high-dimensionality situations. The new tests are based on
the martingale difference divergence covariance (MDD) proposed by Shao and Zhang (2014).
It considers block-wise serial dependence of all lags, therefore, is consistent against general
block-wise nonparametric Pitman’s local alternatives at the parametric rate n−1/2, where n
is the sample size, and free of a user-chosen parameter. In order to cope with the highdimensionality in the sense that the dimension of time series is comparable to or even greater
than the sample size, it is pivotal to employ a bias-reduced estimator for each individual MDD
in the test statistic. Monte Carlo simulations reveal that the bias-reduced statistic generally
performs better than its competitors substantially. Moreover, it is robust to heteroskedasticity
of unknown forms and heavy-tails in the data generating processes. We apply our approach
to test the efficient market hypothesis on the US stock market, using data sets on the monthly
and daily data of portfolios sorted by industry. Our test results provide strong evidence against
the efficient market hypothesis with respect to the US stock market at monthly frequency |
