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ASYMPTOTIC PROPERTIES OF SELF-NORMALIZED LINEAR PROCESSES WITH LONG MEMORY

Published online by Cambridge University Press:  25 November 2011

Magda Peligrad  and
Hailin Sang
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Abstract

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic applications where often the linear processes have long memory, and the innovations have heavy tails.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 3 , June 2012 , pp. 548 - 569
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

The authors are grateful to the referees for carefully reading the paper and for numerous suggestions that significantly improved the presentation of the paper. The first author’s research was supported in part by a Charles Phelps Taft Memorial Fund grant and NSA grants H9823009-1-0005 and H98230-11-1-0135. The second author worked on this paper during visits to the University of Cincinnati and the National Institute of Statistical Sciences.

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