Complete Moment Convergence of Moving Average Processes Generated by Negatively Associated Sequences

- Journal title : Communications for Statistical Applications and Methods
- Volume 17, Issue 4, 2010, pp.507-513
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2010.17.4.507

Title & Authors

Complete Moment Convergence of Moving Average Processes Generated by Negatively Associated Sequences

Ko, Mi-Hwa;

Ko, Mi-Hwa;

Abstract

Let { < 1 < } be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and { < i < } be an absolutely summable sequence of real numbers. Define a moving average process as , n 1 and . In this paper we prove that E||() < implies < and < for all > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 p < 2 and r > 1 + p/2.

Keywords

Moving average process;negatively associated;complete moment convergence;doubly infinite sequence;

Language

English

References

1.

Baek, J. I., Kim, T. S. and Liang, H. Y. (2003). On the convergence of moving average processes under dependent conditions, Australian & New Zealand Journal of Statistics, 45, 331-342.

2.

Burton, R. M. and Dehling, H. (1990). Large deviation for some weakly dependent random processes, Statistics & Probability Letters, 9, 397-401.

3.

Chen, P. Y., Hu, T. H. and Volodin, A. (2009). Limiting behavior of moving average processes under ${\varphi}$ -mixing assumption, Statistics & Probability Letters, 79, 105-111.

4.

Joag-Dev, K. and Proschan, F. (1983). Negative association of random variables with applications, The Annals of Statistics, 11, 286-295.

5.

Kim, T. S. and Baek, J. I. (2001). A central limit theorem for stationary linear processes generated by linearly positively quadrant dependent process, Statistics & Probability Letters, 30, 165-170.

6.

Kim, T. S. and Ko, M. H. (2008). Complete moment convergence of moving average processes under dependence assumptions, Statistics & Probability Letters, 78, 839-846.

7.

Li, D. L., Rao, M. B. and Wang, X. C. (1992). Complete convergence of moving average processes, Statistics & Probability Letters, 14, 111-114.

8.

Li, Y. and Zhang, L. (2004). Complete moment convergence of moving average processes under dependence assumptions, Statistics & Probability Letters, 70, 191-197.

9.

Shao, Q. M. (2000). A comparison theorem on maximum inequalities between negatively associated and independent random variables, Journal of Theoretical Probability, 13, 343-356.