Testing for the Martingale Difference Hypothesis in Multivariate Time Series Models
提出一类基于鞅差散度矩阵的新检验方法，首次用于检验多元时间序列模型的误差项是否为鞅差序列，并给出渐近性质与自助法临界值，适用于计量经济学和金融数据分析。
This article proposes a general class of tests to examine whether the error term is a martingale difference sequence in a multivariate time series model with parametric conditional mean. These new tests are formed based on recently developed martingale difference divergence matrix (MDDM), and they provide formal tools to test the multivariate martingale difference 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 <i>n</i> 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.