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Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes

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  • Eckhard Liebscher
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    Abstract

    In this paper we attempt to establish unified sufficient conditions for geometric ergodicity of autoregressive models. It is shown that there is a close relationship between geometric ergodicity and mixing properties. The case of nonstationary time series is incorporated into the investigations. Several time series models including threshold and EXPARCH-models are examined with respect to geometric ergodicity. In some cases we obtain regions of geometric ergodicity in the parameter space, which are larger than that known from the literature. Copyright 2005 Blackwell Publishing Ltd.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 26 (2005)
    Issue (Month): 5 (09)
    Pages: 669-689

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    Handle: RePEc:bla:jtsera:v:26:y:2005:i:5:p:669-689

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    Cited by:
    1. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    2. Mika Meitz & Pentti Saikkonen, 2010. "A note on the geometric ergodicity of a nonlinear AR–ARCH model," Koç University-TUSIAD Economic Research Forum Working Papers 1003, Koc University-TUSIAD Economic Research Forum.
    3. Dueker, Michael J. & Psaradakis, Zacharias & Sola, Martin & Spagnolo, Fabio, 2011. "Multivariate contemporaneous-threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 160(2), pages 311-325, February.

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