The Annals of Applied Probability

Strong approximation of the empirical process of Garch sequences

István Berkes and Lajos Horváth

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We obtain a strong approximation for the empirical process of n observe delements of a GARCH sequence. The weak convergence of the empirical process and the law of the iterated logarithm are immediate consequences.

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Ann. Appl. Probab., Volume 11, Number 3 (2001), 789-809.

First available in Project Euclid: 5 March 2002

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60G50: Sums of independent random variables; random walks

GARCH ($p, q$) empirical process strong approximation rates of convergence estimates for increments


Berkes, István; Horváth, Lajos. Strong approximation of the empirical process of Garch sequences. Ann. Appl. Probab. 11 (2001), no. 3, 789--809. doi:10.1214/aoap/1015345349.

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