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A Model for Long Memory Conditional Heteroscedasticity

Liudas Giraitis, Peter M. Robinson and Donatas Surgailis
The Annals of Applied Probability
Vol. 10, No. 3 (Aug., 2000), pp. 1002-1024
Stable URL: http://www.jstor.org/stable/2667327
Page Count: 23
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A Model for Long Memory Conditional Heteroscedasticity
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Abstract

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

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