Convergence of Weighted Linear Process for ρ-Mixing Random Variables

Abstract

A central limit theorem and a functional central limit theorem are obtained for weighted linear process of ρ-mixing sequences for the Xt=∑i=0∞aiYt−i, where {Yi, 0≤i<∞} is a sequence of ρ-mixing random variables with EYi=0, 0<EYi2<∞, ∑i=1∞ρ(2i)<∞. The results obtained generalize the results of Liang et al. (2004) to ρ-mixing sequences.