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Probabilistic properties of the Béta-ARCH model

Author

Listed:
  • Jean Diebolt

    (UPMC - Université Pierre et Marie Curie - Paris 6)

  • Dominique Guegan

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

In the present paper we consider the main probabilistic properties of the Markov chain Xt=aXt-1+[a0+(a1+(Xt-1)++a1-(Xt-1) -)2β]1/2εt , that we call the β-ARCH model. We examine the inevitability, irreducibility, Harris recurrence, ergodicity, geometric ergodicity, α-mixing, existence and nonexistence of finite moments and exponential moments of some order and sharp upper bounds for the tails of the stationary density of the process {Xt} in terms of the common density of the εt's.

Suggested Citation

  • Jean Diebolt & Dominique Guegan, 1994. "Probabilistic properties of the Béta-ARCH model," Post-Print halshs-00199490, HAL.
    • Handle: RePEc:hal:journl:halshs-00199490
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    Cited by:

    1. Olivier Habimana, 2017. "Do flexible exchange rates facilitate external adjustment? A dynamic approach with time-varying and asymmetric volatility," International Economics and Economic Policy, Springer, vol. 14(4), pages 625-642, October.

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