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STATIONARY INTEGRATED ARCH(∞) AND AR(∞) PROCESSES WITH FINITE VARIANCE

Published online by Cambridge University Press:  17 October 2017

Liudas Giraitis*
Affiliation:
Queen Mary, London University
Donatas Surgailis
Affiliation:
Vilnius University
Andrius Škarnulis
Affiliation:
Vilnius University
*
*Address correspondence to Liudas Giraitis, School of Economics and Finance, QMUL, Mile End Road, London E1 4NS, UK; e-mail: l.giraitis@qmul.ac.uk.

Abstract

We prove the long standing conjecture of Ding and Granger (1996) about the existence of a stationary Long Memory ARCH model with finite fourth moment. This result follows from the necessary and sufficient conditions for the existence of covariance stationary integrated AR(∞), ARCH(∞), and FIGARCH models obtained in the present article. We also prove that such processes always have long memory.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

The authors are grateful to three anonymous referees, the Co-editor, and the Editor for insightful comments, suggestions, and useful criticisms.

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