Mean vector testing for high dimensional dependent observations

When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve type I error at a given nominal significance level. We propose a new test for the mean vector when the dimension increases linearly with sample size and the data is a realization of an M -dependent stationary process. The order M is also allowed to increase with the sample size. Asymptotic normality of the test statistic is derived by extending the central limit theorem result for M -dependent processes using two dimensional triangular arrays. Finite sample simulation results indicate the cost of ignoring dependence amongst observations.