Complete convergence of moving average processes under dependence assumptions
type: Item
instance of: scholarly article
title: Complete convergence of moving average processes under dependence assumptions
zbMATH Open document ID: 0873.60019
DOI: 10.1016/0167-7152(95)00215-4
published in: Statistics \& Probability Letters
publication date: 1997-10-26T00:00:00Z
review text: The author considers a moving-average process \(X_k=\sum_{i=-\infty}^\infty a_{i+k}Y_i\), \(k\geq 1\), for an absolutely summable sequence \(\{a_i\}\) of real numbers and a doubly infinite sequence \(\{Y_i\}\) of identically distributed and \(\varphi\)-mixing random variables. Under a slight condition on the \(\varphi\)-mixing coefficient and \(EY_1=0\), \(E|Y_1|^{rt}<\infty\) for \(1\leq t<2\), \(r\geq 1\), the convergence of the series \(\sum_{n=1}^\infty n^{r-2}P(|\sum_{k=1}^n X_k|\geq n^{1/t}\varepsilon)\) for all \(\varepsilon>0\) could be proved.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60G05
zbMATH DE Number: 954945
zbMATH Keywords: complete convergence
zbMATH Keywords: phi-mixing
zbMATH Keywords: moving-average process
author: Lixin Zhang
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
full work available at URL: 0167-7152(95)00215-4
OpenAlex ID: W2041161697
cites work: Large deviations for some weakly dependent random processes
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cites work: Complete convergence of moving average processes
cites work: Q3476066
cites work: Almost sure invariance principles for mixing sequences of random variables
description: scientific article; zbMATH DE number 954945