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L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term

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  • Lu, Zudi
  • Jiang, Zhenyu
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    Abstract

    In this note, the condition to ensure the L1 geometric ergodicity of a multivariate nonlinear AR model mixed with an ARCH term (also called conditional heteroscedastic autoregressive nonlinear model) is investigated. Under some mild conditions on the white noise process with first absolute moment, a sufficient condition much weaker than that by Ango Nze (C.R. Acad. Sci. Paris 315 ser. 1 (1992) 1301-1304) is derived. As an application, the L1 geometric ergodicity of an additive AR model mixed with a multiplicative ARCH term is studied. Our condition expands the application of the result in Ango Nze (C.R. Acad. Sci. Paris 315 ser. 1 (1992) 1301-1304) and is interesting for robust modeling when the white noise is fat-tailed with infinite variance. Some additional remarks are also made.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 51 (2001)
    Issue (Month): 2 (January)
    Pages: 121-130

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    Handle: RePEc:eee:stapro:v:51:y:2001:i:2:p:121-130

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    Related research

    Keywords: Autoregression Conditional heteroscedasticity L1 geometric ergodicity Markov chain Multivariate AR-ARCH (CHARN) model;

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    Cited by:
    1. Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
    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. Mika Meitz & Pentti Saikkonen, 2007. "Stability of nonlinear AR-GARCH models," Economics Series Working Papers 328, University of Oxford, Department of Economics.
    4. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.
    5. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(01), pages 37-70, February.

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