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A0231
Title: Testing for the martingale difference hypothesis in multivariate time series models Authors:  Ke Zhu - University of Hong Kong (Hong Kong) [presenting]
Abstract: A general class of tests is proposed to examine whether the error term is a martingale difference sequence in a multivariate time series model with a parametric conditional mean. These new tests are formed based on the recently developed martingale difference divergence matrix (MDDM). They provide formal tools to test the multivariate martingale hypothesis in the literature for the first time. Under suitable conditions, the asymptotic null distributions of these MDDM-based tests are established. Moreover, these MDDM-based tests are consistent to detect a broad class of fixed alternatives and have nontrivial power against local alternatives of order $n^{-1/2}$, where $n$ is the sample size. Since the asymptotic null distributions depend on the data generating process and the parameter estimation, a wild bootstrap procedure is further proposed to approximate the critical values of these MDDM-based tests, and its theoretical validity is justified. Finally, the usefulness of these MDDM-based tests is illustrated by simulation studies and one real data example.