Central limit theorem for linear processes

Abstract

In this paper we study the CLT for partial sums of a generalized linear process $X_n = \sum_{i=1}^n a_{ni} \xi_i$, where $\sup_n \sum_{i=1}^n a_{ni}^2 < \infty, \max_{1 \leq i \leq n}are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.