ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES

Mi-Hwa Ko, Tae-Sung Kim, Dae-Hee Ryu
2008 Communications of the Korean Mathematical Society  
Let {Y i ; −∞ < i < ∞} be a doubly infinite sequence of identically distributed and ρ * -mixing random variables with zero means and finite variances and {a i ; −∞ < i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of { P n k=1 P ∞ i=−∞ a i+k Y i /n 1/p ; n ≥ 1} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence
more » ... nder dependence assumptions, Statist. Probab. Lett. 70 (2004), 191-197.] to the ρ * -mixing case.
doi:10.4134/ckms.2008.23.4.597 fatcat:m6bmyp6275cmda77d6okirmz4u