Complete moment convergence of moving-average processes under END assumptions

Abstract

Let $\{Y_i;-\infty <i<\infty \}$ be a doubly infinite sequence of identically distributed and extended negatively dependent random variables with zero means and finite variance and $\{a_i;-\infty <i<\infty \}$ be an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of the moving-average process $X_k={\sum }_{i=-\infty }^{\infty }{a}_{i+k}{Y}_i,$ and extend to the m-extended negatively dependent case.

Keywords:

• Moving-average process
• complete moment convergence
• extended negatively dependent

2010 Mathematics Subject Classification:

• 60F15

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11471104].