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Long memory properties and covariance structureof the EGARCH model

Published online by Cambridge University Press:  15 November 2002

Donatas Surgailis  and
Marie-Claude Viano
Donatas Surgailis
Affiliation:
Vilnius Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania; [email protected].
Marie-Claude Viano
Affiliation:
Université des Sciences et Technologies de Lille, 59655 Villeneuve-d'Ascq Cedex, France; [email protected].
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Abstract

The EGARCH model of Nelson [29] is one of the most successfulARCH models which may exhibit characteristic asymmetries offinancial time series, as well as long memory. The paper studiesthe covariance structure and dependence properties of the EGARCHand some related stochastic volatility models. We show that thelarge time behavior of the covariance of powers of the (observed)ARCH process is determined by the behavior of the covariance ofthe (linear) log-volatility process; in particular, a hyperbolicdecay of the later covariance implies a similar hyperbolic decayof the former covariances. We show, in this case, that normalizedpartial sums of powers of the observed process tend to fractionalBrownian motion. The paper also obtains a (functional) CLT for thecorresponding partial sums' processes of the EGARCH model withshort and moderate memory. These results are applied to studyasymptotic behavior of tests for long memory using the R/Sstatistic.

Keywords

EGARCH modelslong-memorypartial sumsrescaled range.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 311 - 329
Copyright
© EDP Sciences, SMAI, 2002

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