Limit theorems for locally stationary processes

Abstract

We present limit theorems for locally stationary processes that have a one sided time-varying moving average representation. In particular, we prove a central limit theorem (CLT), a weak and a strong law of large numbers (WLLN, SLLN) and a law of the iterated logarithm (LIL) under mild assumptions that are closely related to those originally imposed by Dahlhaus and Polonik (2006).