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

Published online by Cambridge University Press:  30 September 2009

Liudas Giraitis ,
Remigijus Leipus  and
Donatas Surgailis
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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.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 2 , April 2010 , pp. 406 - 425
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The authors are grateful to the referee and the associated editor for useful comments. Giraitis was supported by the ESRC grant RES062230790. The research of Leipus and Surgailis was supported by the bilateral France-Lithuania scientific project Gilibert. Surgailis was supported by the Lithuanian State Science and Studies Foundation grant no. T-70/09. Part of the paper was written while Surgailis was visiting the Department of Economics, Queen Mary, University of London. Surgailis would like to thank the university for support and providing an ideal working environment.

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