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ASYMPTOTIC PROPERTIES OF SELF-NORMALIZEDLINEAR 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 fractionalBrownian motion for long memory time series havingindependent innovations with infinite second moment.For the sake of applications we derive theself-normalized version of this theorem. The studyis motivated by models arising in economicapplications where often the linear processes havelong memory, and the innovations have heavytails.

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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 forcarefully reading the paper and for numeroussuggestions that significantly improved thepresentation of the paper. The first author’sresearch was supported in part by a Charles PhelpsTaft Memorial Fund grant and NSA grantsH9823009-1-0005 and H98230-11-1-0135. The secondauthor worked on this paper during visits to theUniversity of Cincinnati and the NationalInstitute of Statistical Sciences.

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