Abstract
Let \(\{Y_{i},-\infty< i<\infty\}\) be a sequence of \(\rho^{-}\)-mixing random variables without the assumption of identical distributions, and \(\{a_{i},-\infty< i<\infty\}\) be an absolutely summable sequence of real numbers. In this paper, under some suitable conditions, we establish the complete moment convergence for the partial sum of moving average processes \(\{X_{n}=\sum_{i=-\infty}^{\infty}a_{i}Y_{i+n},n\geq 1\}\). These results promote and improve the corresponding results obtained by Li and Zhang (Stat. Probab. Lett. 70:191-197, 2004) from NA to the case of a \(\rho^{-}\)-mixing setting.
Highlights
Chen et al [ ], Guo [ ], Kim et al [ , ], Ko et al [ ], Li et al [ ], Li and Zhang [ ], Qiu et al [ ], Wang and Hu [ ], Yang and Hu [ ], Zhang [ ], Zhen et al [ ], Zhou et al [ ], Zhou and Lin [ ], Shen et al [ ] have obtained the complete (moment) convergence of moving average process based on a sequence of dependent (or mixing) random variables, respectively
Let {Yi, –∞ < i < ∞} be a sequence of random variables and {ai, –∞ < i < ∞} be an absolutely summable sequence of real numbers, and for n ≥ set Xn = ai Yi+n .The limit behavior of the moving average process {Xn, n ≥ } has been extensively investigated by many authors
[ ] has established the central limit theorem, Račkauskas and Suquet [ ] have proved the functional central limit theorems for self-normalized partial sums of linear processes, and
Summary
Chen et al [ ], Guo [ ], Kim et al [ , ], Ko et al [ ], Li et al [ ], Li and Zhang [ ], Qiu et al [ ], Wang and Hu [ ], Yang and Hu [ ], Zhang [ ], Zhen et al [ ], Zhou et al [ ], Zhou and Lin [ ], Shen et al [ ] have obtained the complete (moment) convergence of moving average process based on a sequence of dependent (or mixing) random variables, respectively. Very few results for moving average process based on a ρ–-mixing random variables are known. Li and Zhang [ ] obtained the following complete moment convergence of moving average processes under NA assumptions.
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