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The mixing property of bilinear and generalised random coefficient autoregressive models

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  • Dinh Tuan, Pham

Abstract

The paper gives sufficient conditions for the absolute regularity of bilinear models. Our approach is based on their Markovian representation. The above property is a direct consequence of the geometric ergodicity of the Markovian process in this representation. The latter process belongs to what we call the generalised random coefficients autoregressive models. Conditions for the geometric ergodicity and also for the existence of moments for this model are given. Our results generalise that of Feigin and Tweedie.

Suggested Citation

  • Dinh Tuan, Pham, 1986. "The mixing property of bilinear and generalised random coefficient autoregressive models," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 291-300, December.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:2:p:291-300
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    Cited by:

    1. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.
    2. Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    3. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    4. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(1), pages 37-70, February.
    5. Filippo Altissimo & Giovanni L. Violante, 2001. "The non-linear dynamics of output and unemployment in the U.S," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 461-486.
    6. J. Terpstra & M. Rao, 2001. "Generalized Rank Estimates For An Autoregressive Time Series: A U-Statistic Approach," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 155-179, May.

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