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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

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.

Suggested Citation

  • Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, September.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:5:p:669-689
    DOI: 10.1111/j.1467-9892.2005.00412.x
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    References listed on IDEAS

    as
    1. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    2. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    4. Peter J. Brockwell & Jian Liu & Richard L. Tweedie, 1992. "On The Existence Of Stationary Threshold Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(2), pages 95-107, March.
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    Cited by:

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    4. 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.
    5. 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.
    6. 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.
    7. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
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    9. Zhou, Yunzhe & Shi, Chengchun & Li, Lexin & Yao, Qiwei, 2023. "Testing for the Markov property in time series via deep conditional generative learning," LSE Research Online Documents on Economics 119352, London School of Economics and Political Science, LSE Library.
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    11. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, vol. 3(1), pages 1-53, January.
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