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On The Existence Of Stationary Threshold Autoregressive Moving‐Average Processes

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  • Peter J. Brockwell
  • Jian Liu
  • Richard L. Tweedie

Abstract

. Conditions for the existence of causal and strictly stationary solutions of the equations defining a self‐exciting threshold autoregressive moving‐average (SETARMA) model are derived. For threshold autoregressive models we allow the autoregressive coefficients to be random and derive sufficient conditions for geometric ergodicity and the existence of strictly and weakly stationary solutions of the defining equations.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:13:y:1992:i:2:p:95-107
    DOI: 10.1111/j.1467-9892.1992.tb00096.x
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    Cited by:

    1. 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.
    2. Yaxing Yang & Shiqing Ling, 2018. "A Note On The Lse Of Three-Regime Tar Model With An Infinite Variance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-13, June.
    3. Xiaobing Zheng & Kun Liang & Qiang Xia & Dabin Zhang, 2022. "Best Subset Selection for Double-Threshold-Variable Autoregressive Moving-Average Models: The Bayesian Approach," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1175-1201, March.
    4. Ahmed Ghezal & Maddalena Cavicchioli & Imane Zemmouri, 2024. "On the existence of stationary threshold bilinear processes," Statistical Papers, Springer, vol. 65(6), pages 3739-3767, August.
    5. Greta Goracci, 2021. "An empirical study on the parsimony and descriptive power of TARMA models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 109-137, March.

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