Some results for empirical processes of locally dependent time series

In this paper we derive some fundamental properties of locally dependent time series of order m(n), where m(n) is allowed to tend to infinity with the sample size n. More specifically we consider a central limit theorem, an exponential inequality for the local fluctuations of the empirical process, and weak convergence of the empirical process. Locally dependent time series are of independent interest, but they may also serve as useful approximations to other stochastic processes. Some applications are briefly indicated.