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STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

Published online by Cambridge University Press:  01 February 2000

Liudas Giraitis ,
Piotr Kokoszka  and
Remigijus Leipus
Liudas Giraitis
Affiliation:
London School of Economics
Piotr Kokoszka
Affiliation:
University of Liverpool
Remigijus Leipus
Affiliation:
University of Liverpool
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Abstract

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

Type
Research Article
Information
Econometric Theory , Volume 16 , Issue 1 , February 2000 , pp. 3 - 22
Copyright
© 2000 Cambridge University Press

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