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On square-integrability of an AR process with Markov switching

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  • Yao, J.

Abstract

For an autoregressive process with Markov switching, we give a condition ensuring the existence of a square-integrable stationary solution. Unlike conditions based on top Lyapounov exponents, our condition is directly expressed in terms of the parameters of the model. Specific examples are also provided to give more details on this condition.

Suggested Citation

  • Yao, J., 2001. "On square-integrability of an AR process with Markov switching," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 265-270, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:3:p:265-270
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    References listed on IDEAS

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    1. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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    5. Ulla Holst & Georg Lindgren & Jan Holst & Mikael Thuvesholmen, 1994. "Recursive Estimation In Switching Autoregressions With A Markov Regime," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 489-506, September.
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    Cited by:

    1. Psaradakis Zacharias & Spagnolo Nicola, 2002. "Power Properties of Nonlinearity Tests for Time Series with Markov Regimes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-16, November.
    2. Zacharias Psaradakis & Nicola Spagnolo, 2003. "On The Determination Of The Number Of Regimes In Markov‐Switching Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 237-252, March.
    3. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.
    4. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    5. Aknouche, Abdelhakim, 2024. "Periodically homogeneous Markov chains: The discrete state space case," MPRA Paper 122287, University Library of Munich, Germany.
    6. Valerie Girardin & Rachid Senoussi, 2020. "Filling the gap between Continuous and Discrete Time Dynamics of Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 590-602, July.
    7. Maximo Camacho, 2002. "Nonlinear stochastic trends and economic fluctuations," Computing in Economics and Finance 2002 274, Society for Computational Economics.
    8. Chaojun Li & Yan Liu, 2020. "Asymptotic Properties of the Maximum Likelihood Estimator in Regime-Switching Models with Time-Varying Transition Probabilities," Papers 2010.04930, arXiv.org, revised Dec 2021.
    9. Camacho, Maximo, 2005. "Markov-switching stochastic trends and economic fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 135-158, January.
    10. Zacharias Psaradakis & Fabio Spagnolo, 2005. "Forecast performance of nonlinear error-correction models with multiple regimes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(2), pages 119-138.
    11. Aaron D. Smallwood, 2016. "A Monte Carlo Investigation of Unit Root Tests and Long Memory in Detecting Mean Reversion in I(0) Regime Switching, Structural Break, and Nonlinear Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 986-1012, June.

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