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August 2000 A model for long memory conditional heteroscedasticity
Liudas Giraitis, Peter M. Robinson, Donatas Surgailis
Ann. Appl. Probab. 10(3): 1002-1024 (August 2000). DOI: 10.1214/aoap/1019487516

Abstract

or a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence $r_t$ is the square of an inhomogeneous linear combination of $r_s, s < t$, we give conditions under which, for integers $l \geq 2, r_t^l$ has long memory autocorrelation and normalized partial sums of $r_t^l$ converge to fractional Brownian motion.

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Liudas Giraitis. Peter M. Robinson. Donatas Surgailis. "A model for long memory conditional heteroscedasticity." Ann. Appl. Probab. 10 (3) 1002 - 1024, August 2000. https://doi.org/10.1214/aoap/1019487516

Information

Published: August 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1084.62516
MathSciNet: MR1789986
Digital Object Identifier: 10.1214/aoap/1019487516

Subjects:
Primary: 62M10
Secondary: 60G18

Keywords: ARCH processes , central limit theorem , diagrams , fractioinal Brownian motion , long memory , Volterra series

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August 2000
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