[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2012.49.2.235

PRECISE ASYMPTOTICS OF MOVING AVERAGE PROCESS UNDER ?-MIXING ASSUMPTION

Li, Jie (School of Mathematics and Statistics Zhejiang University of Finance and Economics)

Publication Information

Journal of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 235-249 More about this Journal

Abstract

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$ -mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

Keywords

complete moment convergence; moving average; $\phi$ -mixing; precise asymptotics;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 1

Reference

1	P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
2	R. M. Burton and H. Dehling, Large deviations for some weakly dependent random process, Statist. Probab. Lett. 9 (1990), no. 5, 397-401. DOI ScienceOn
3	P. L. Hsu and H. Robbins, Complete convergence and the strong law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31. DOI ScienceOn
4	D. L. Li, M. B. Rao, and X. C. Wang, Complete convergence of moving average processes, Statist. Probab. Lett. 14 (1992), no. 2, 111-114. DOI ScienceOn
5	Y. X. Li, Precise asymptotics in the law of large numbers of moving-average processes, Acta Math. Sci. Ser. A Chin. Ed. 26 (2006), no. 5, 675-687.
6	W. D. Liu and Z. Y. Lin, Precise asymptotics for a new kind of complete moment convergence, Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799. DOI ScienceOn
7	Q. M. Shao, A moment inequality and its application, Acta Math. Sinica 31 (1988), no. 6, 736-747.
8	X. Y. Yang, The law of the iterated logarithm and the central limit theorem with random indices for B-valued stationary linear processes, Chinese Ann. Math. Ser. A 17 (1996), no. 6, 703-714.
9	L. X. Zhang, Complete convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 30 (1996), no. 2, 165-170. DOI ScienceOn