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AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS

Published online by Cambridge University Press:  30 September 2009

Liudas Giraitis*
Affiliation:
Queen Mary, University of London
Remigijus Leipus
Affiliation:
Vilnius University and Institute of Mathematics and Informatics
Donatas Surgailis
Affiliation:
Vilnius University and Institute of Mathematics and Informatics
*Corresponding
*Address correspondence to Liudas Giraitis, Queen Mary, University of London, Department of Economics, Mile End Road, London E1 4NS; e-mail: L.Giraitis@qmul.ac.uk.

Abstract

The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH) model as defined in (1), which was introduced in Robinson (1991) and studied in Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting aggregate of the (G)eneralized LARCH(1,1) process in (3)–(4) with random Beta distributed coefficient β exhibits long memory. In particular, we prove that squares of the limiting aggregated process have slowly decaying correlations and their partial sums converge to a self-similar process of a new type.

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Copyright
Copyright © Cambridge University Press 2009

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