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STATIONARY ARCH MODELS: DEPENDENCE STRUCTURE AND CENTRAL LIMIT THEOREM

  • Liudas Giraitis (a1), Piotr Kokoszka (a2) and Remigijus Leipus (a2)
    • Published online: 01 February 2000
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.

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Corresponding author
Address correspondence to: Piotr Kokoszka, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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