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AGGREGATION OF THE RANDOM COEFFICIENTGLARCH(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 theLinear ARCH (LARCH) model as defined in (1), whichwas introduced in Robinson (1991) and studied inGiraitis, Robinson, and Surgailis (2000) and otherworks. We show that the limiting aggregate of the(G)eneralized LARCH(1,1) process in (3)–(4) withrandom Beta distributed coefficientβ exhibits long memory. Inparticular, we prove that squares of the limitingaggregated process have slowly decaying correlationsand their partial sums converge to a self-similarprocess of a new type.

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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 theassociated editor for useful comments. Giraitiswas supported by the ESRC grant RES062230790. Theresearch of Leipus and Surgailis was supported bythe bilateral France-Lithuania scientific projectGilibert. Surgailis was supported by theLithuanian State Science and Studies Foundationgrant no. T-70/09. Part of the paper was writtenwhile Surgailis was visiting the Department ofEconomics, Queen Mary, University of London.Surgailis would like to thank the university forsupport and providing an ideal workingenvironment.

References

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