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Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)–Processes

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Handbook of Financial Time Series

Abstract

This paper collects some of the well known probabilistic properties of GARCH (p, q) processes. In particular, we address the question of strictly and of weakly stationary solutions. We further investigate moment conditions as well as the strong mixing property of GARCH processes. Some distributional properties such as the tail behaviour and continuity properties of the stationary distribution are also included.

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  1. Technische Universität Braunschweig, Institut für Mathematische Stochastik, Pockelsstrasse, 14, D-38106, Braunschweig

    Alexander M. Lindner

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    Lindner, A.M. (2009). Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)–Processes. 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_2

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