STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM
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- 1 February 2000
- journal article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 16 (1) , 3-22
- https://doi.org/10.1017/s0266466600161018
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.Keywords
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