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ARCH(∞) Models and Long Memory Properties

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Handbook of Financial Time Series

Abstract

ARCH(∞)-models are a natural nonparametric generalization of the class of GARCH(p, q) models which exhibit a rich covariance structure (in particular, hyperbolic decay of the autocovariance function is possible). We discuss stationarity, long memory properties and the limit behavior of partial sums of ARCH(∞) processes as well as some of their modifications (linear ARCH and bilinear models).

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Authors and Affiliations

  1. Department of Economics, Queen Mary, University of London, , Mile End Road, London, E1 4NS, U.K.

    Liudas Giraitis

  2. Lithuania, and Institute of Mathematics and Informatics, Vilnius University, Naugarduko, 24, Vilnius, 03225, Akademijos 4, LT-08663 Vilnius, Lithuania

    Remigijus Leipus & Donatas Surgailis

Authors
  1. Liudas Giraitis
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  2. Remigijus Leipus
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  3. Donatas Surgailis
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Correspondence to Liudas Giraitis .

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    Giraitis, L., Leipus, R., Surgailis, D. (2009). ARCH(∞) Models and Long Memory Properties. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_3

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