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Measures of Dependence for Stable AR(1) Models with Time-Varying Coefficients 

Authors: J. Nowicka-Zagrajek a; A. Wylstrokomanacuteska a
Affiliation:   a Institute of Mathematics and Computer Science, Wroclstrokaw University of Technology, Poland
DOI: 10.1080/15326340701826906
Publication Frequency: 4 issues per year
Published in: journal Stochastic Models, Volume 24, Issue 1 January 2008 , pages 58 - 70
Formats available: HTML (English) : PDF (English)
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Abstract

In this paper we study the dependence structure for AR(1) models with symmetric agr-stable innovations and time-varying coefficients. In this case the covariance function is not defined and therefore other measures of dependence have to be used. We formulate conditions providing the bounded solutions of such systems and give the form of the solution. Then the covariation and the codifference for stable AR(1) models are studied and the asymptotic relation between these two measures of dependence for the considered models is examined.
Keywords: AR models; Codifference; Covariation; Dependence structure; Stable random variables
AMS Subject Classification: 60G52; 60H35; 91B70
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