A0835
Title: Testing the martingale difference hypothesis in high dimension
Authors: Qing Jiang - Beijing Normal University (China) [presenting]
Abstract: The aim is to test the martingale difference hypothesis for high-dimensional time series. The test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, the null distribution of the test statistic is approximated by Gaussian approximation and a simulation-based approach to generate critical values is provided. The asymptotic behaviour of the test statistic under the alternative is also studied. This approach is nonparametric as the null hypothesis only assumes the time series concerned is martingale difference without specifying any parametric forms of its conditional moments. As an advantage of Gaussian approximation, the test is robust to the cross-series dependence of unknown magnitude. To the best of our knowledge, this is the first valid test for the martingale difference hypothesis that not only allows for large dimensions but also captures nonlinear serial dependence. The practical usefulness of the test is illustrated via simulation and real data analysis. The test is implemented in a user-friendly R-function.
