Some mixing properties of time series models
type: Item
instance of: scholarly article
title: Some mixing properties of time series models
zbMATH Open document ID: 0564.62068
DOI: 10.1016/0304-4149(85)90031-6
author: Tuan D. Pham
author: Lanh Tat Tran
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: \textit{J. L. Gastwirth} and \textit{H. Rubin} [Ann. Stat. 3, 809-824 (1975; Zbl 0318.62016)] introduced the so-called Gastwirth and Rubin mixing condition in a study of the large sample behaviour of estimators for dependent processes, mainly because first-order autoregressive processes do not satisfy the more popular \(\phi\)-mixing condition. The Gastwirth and Rubin mixing condition is intermediate between strong mixing (which is weaker) and \(\phi\)-mixing, and contains absolute regularity as a particular case. The present paper brings a substantial support to the statistical relevance of the Gastwirth and Rubin condition by showing that it is satisfied by usual ARMA processes. This result is of great theoretical importance in time series analysis, since the vast literature on absolute regular processes can now be used in this area.
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 3899991
zbMATH Keywords: mixing rates
zbMATH Keywords: linear processes
zbMATH Keywords: weakly dependent processes
zbMATH Keywords: Gastwirth and Rubin mixing condition
zbMATH Keywords: absolute regularity
zbMATH Keywords: ARMA processes
zbMATH Keywords: time series
zbMATH Keywords: absolute regular processes
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90031-6
OpenAlex ID: W1989089774
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description: scientific article; zbMATH DE number 3899991