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Zbl 1247.60043
Yang, Wenzhi; Wang, Xuejun; Ling, Nengxiang; Hu, Shuhe
On complete convergence of moving average process for AANA sequence.
(English)
[J] Discrete Dyn. Nat. Soc. 2012, Article ID 863931, 24 p. (2012). ISSN 1026-0226; ISSN 1607-887X/e

Summary: We investigate the moving average process such that $X_n = \sum^\infty_{i=1} a_i Y_{i+n}, n \geq 1$, where $\sum^\infty_{i=1} |a_i| < \infty$ and $\{Y_i, 1 \leq i < \infty\}$ is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.
MSC 2000:
*60F15 Strong limit theorems
60G10 Stationary processes

Keywords: moving average process; sequence of asymptotically almost negatively associated (AANA) random variables; complete convergence; complete moment convergence

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