Limiting behaviour of moving average processes based on a sequence of \(\rho^{-}\) mixing and negatively associated random variables. (English) Zbl 1132.60028

Budsaba, Kamon; Chen, Pingyan; Volodin, Andrei

Lobachevskii J. Math. 26, 17-25 (2007).

Summary: Let \(\{Y_i, -\infty < i < \infty\}\) be a doubly infinite sequence of identically distributed \(\rho^{-}\)-mixing or negatively associated random variables, \(\{a_i, -\infty<i <\infty\}\) a sequence of real numbers. In this paper, we prove the rate of convergence and strong law of large numbers for the partial sums of moving average processes \(\{\sum^{\infty}_{i=-\infty}a_iY_{i+n},n\geq 1\}\), under some moment conditions.

MSC:

60F15

Strong limit theorems

Keywords:

rate of convergence; strong law of large numbers; moment conditions