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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

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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.

Information

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

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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