Complete moment convergence of moving average processes for m-WOD sequence

Abstract

Abstract In this paper, the complete moment convergence for the partial sum of moving average processes { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } $\{X_{n}=\sum_{i=-\infty }^{\infty }a_{i}Y_{i+n},n\geq 1\}$ is established under some mild conditions, where { Y i , − ∞ < i < ∞ } $\{Y_{i},-\infty < i<\infty \}$ is a sequence of m-widely orthant dependent (m-WOD, for short) random variables which is stochastically dominated by a random variable Y, and { a i , − ∞ < i < ∞ } $\{a_{i},-\infty < i<\infty \}$ is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results from m-extended negatively dependent (m-END, for short) sequences to m-WOD sequences.

Keywords

• Moving average processes
• m-WOD
• Complete moment convergence