Limiting Behavior of Moving Average Processes Based on a Sequence of ρ- Mixing Random Variables

Authors

  • Kamon Budsaba Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Bangkok 12121, Thailand.
  • Pingyan Chen Department of Mathematics, Jinan University, Guangzhou 510630, China
  • Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada.

Keywords:

complete convergence, Marcinkiewicz-Zygmund strong laws of large numbers, moving average process, ρ− -mixing, ρ *-mixing, negative association

Abstract

Let {Y ,−∞ < i < ∞} i be a doubly infinite sequence of identically distributed ρ− -mixing random variables, {ai ,−∞ < i < ∞} i an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and MarcinkiewiczZygmund strong law of large numbers for the partial sums of moving average processes \left\{\begin{matrix} & & \\ & & \\ & & \end{matrix}\right.\sum_{i=-\infty }^{\infty }\inline a_{i} Y_{i+n},n\geq 1 \left.\begin{matrix} & & \\ & & \\ & & \end{matrix}\right\} under the same conditions as the case of the usual partial sums.

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How to Cite

Budsaba, K., Chen, P., & Volodin, A. (2015). Limiting Behavior of Moving Average Processes Based on a Sequence of ρ- Mixing Random Variables. Thailand Statistician, 5, 69–80. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34355

Issue

Vol. 5 (2007): JULY

Section

Articles