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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

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.

Suggested Citation

  • Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:2:p:121-130
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    Cited by:

    1. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. 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(5), pages 1291-1320, October.
    3. Meitz, Mika & Saikkonen, Pentti, 2010. "A note on the geometric ergodicity of a nonlinear AR-ARCH model," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 631-638, April.
    4. Zhu, Huafeng & Zhang, Xingfa & Liang, Xin & Li, Yuan, 2017. "On a vector double autoregressive model," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 86-95.
    5. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
    6. Levine, Michael & Li, Jinguang (Tony), 2012. "A simple additivity test for conditionally heteroscedastic nonlinear autoregression," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2421-2429.
    7. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    8. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(1), pages 37-70, February.
    9. 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.

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    More about this item

    Keywords

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

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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