Econometric Theory

Table of Contents - 2000 - Volume 16, Issue 01  


STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

Liudas  Giraitis a1, Piotr  Kokoszka a2c1 and Remigijus  Leipus a2
a1 London School of Economics
a2 University of Liverpool

Abstract

This paper studies a broad class of nonnegative ARCH([infty infinity]) 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.


Correspondence:
c1 Address correspondence to: Piotr Kokoszka, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom.

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