The Annals of Applied Probability

A model for long memory conditional heteroscedasticity

Liudas Giraitis, Peter M. Robinson, and Donatas Surgailis

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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.

Article information

Ann. Appl. Probab., Volume 10, Number 3 (2000), 1002-1024.

First available in Project Euclid: 22 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G18: Self-similar processes

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


Giraitis, Liudas; Robinson, Peter M.; Surgailis, Donatas. A model for long memory conditional heteroscedasticity. Ann. Appl. Probab. 10 (2000), no. 3, 1002--1024. doi:10.1214/aoap/1019487516.

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