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aug 2006 Strong approximation for the sums of squares of augmented GARCH sequences
Alexander Aue, István Berkes, Lajos Horváth
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Bernoulli 12(4): 583-608 (aug 2006). DOI: 10.3150/bj/1155735928


We study so-called augmented GARCH sequences, which include many submodels of considerable interest, such as polynomial and exponential GARCH. To model the returns of speculative assets, it is particularly important to understand the behaviour of the squares of the observations. The main aim of this paper is to present a strong approximation for the sum of the squares. This will be achieved by an approximation of the volatility sequence with a sequence of blockwise independent random variables. Furthermore, we derive a necessary and sufficient condition for the existence of a unique (strictly) stationary solution of the general augmented GARCH equations. Also, necessary and sufficient conditions for the finiteness of moments are provided.


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Alexander Aue. István Berkes. Lajos Horváth. "Strong approximation for the sums of squares of augmented GARCH sequences." Bernoulli 12 (4) 583 - 608, aug 2006.


Published: aug 2006
First available in Project Euclid: 16 August 2006

zbMATH: 1125.62092
MathSciNet: MR2248229
Digital Object Identifier: 10.3150/bj/1155735928

Keywords: augmented GARCH processes , moments , partial sums , stationary solutions , strong approximation

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 4 • aug 2006
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