Asymptotics for moving average processes with dependent innovations
type: Item
instance of: scholarly article
title: Asymptotics for moving average processes with dependent innovations
zbMATH Open document ID: 0996.60041
DOI: 10.1016/S0167-7152(00)00195-4
author: Qiying Wang
author: Yan-Xia Lin
author: Chandra M. Gulati
published in: Statistics \& Probability Letters
publication date: 2002-10-23T00:00:00Z
review text: The authors consider a linear process \(X_t=\sum_{k=0}^\infty \psi_k \varepsilon_{t-k}\) with centered random variables \(\varepsilon_k\). Functional limit theorems for suitably normalized partial sums of \((X_t)\) are investigated in two cases. On one hand, the long memory case where \(\psi_k=k^{-\alpha} \ell(k)\) with \(\alpha \in (1/2,1)\) and a slowly varying function \(\ell(.)\) is studied. In contrast to known results from the literature with independent innovations \((\varepsilon_k)\), it is assumed in this paper that they form a martingale difference sequence. On the other hand ordinary linear processes with \((\psi_k) \in \ell_1\) and innovations \((\varepsilon_k)\) forming a martingale difference sequence or satisfy some mixing conditions are considered.
reviewed by: Ulrich Stadtmüller
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 1697552
zbMATH Keywords: linear process
zbMATH Keywords: long memory process
zbMATH Keywords: functional limit theorem
MaRDI profile type: Publication
cites work: Noncentral limit theorems and Appell polynomials
cites work: Q4865042
cites work: Q5560061
cites work: Q3827448
cites work: The Invariance Principle for Stationary Processes
cites work: Q4884570
cites work: AN INTRODUCTION TO LONG-MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING
cites work: Q3911791
cites work: The central limit theorem for time series regression
cites work: Fractional differencing
cites work: Fractional Brownian Motions, Fractional Noises and Applications
cites work: Q4220495
cites work: Hyperbolic Decay Time Series
cites work: Invariance principles for mixing sequences of random variables
cites work: Central limit theorem for linear processes
cites work: Asymptotics for linear processes
cites work: Q3476066
cites work: Maximal inequalities for partial sums of \(\rho\)-mixing sequences
cites work: The Fractional Unit Root Distribution
cites work: ASYMPTOTIC BEHAVIOUR OF DISCRETE LINEAR PROCESSES
cites work: Some Results on the Complete and Almost Sure Convergence of Linear Combinations of Independent Random Variables and Martingale Differences
cites work: Weak convergence to fractional brownian motion and to the rosenblatt process
cites work: On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes
Wikidata QID: Q126632557
full work available at URL: s0167-7152(00)00195-4
OpenAlex ID: W1967524437
description: scientific article; zbMATH DE number 1697552