Complete q-order moment convergence of moving average processes under φ-mixing assumptions

Abstract

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 average processes \(\left\{ {X_n = \sum\limits_{i = - \infty }^\infty {a_i + Y_{i + n} ,n \geqslant 1} } \right\}\) based on the sequence {Y i , −∞ < i < ∞} of φ-mixing random variables under some suitable conditions. These results generalize and complement earlier results.