COMPLETE q-ORDER MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES UNDER φ-MIXING ASSUMPTIONS

摘要

Let {Y_i, -∞ ＜ i ＜ ∞} be a doubly infinite sequence of identically distributed φ-mixing random variables, and {a_i, -∞ ＜ i ＜ ∞} an absolutely summable sequence of real numbers. We prove the complete q-order moment convergence for the partial sums of moving {X_n = ∞Σi=-∞ a_iY_(i+n), n ≥ 1} based on the sequence {Y_i, -∞ ＜ i ＜ ∞} of φ-mixing random variables under some suitable conditions. These results generalize and complement earlier results.