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Hysteretic autoregressive time series models

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  • Guodong Li
  • Bo Guan
  • Wai Keung Li
  • Philip L. H. Yu

Abstract

This paper extends the classical two-regime threshold autoregressive model by introducing hysteresis to its regime-switching structure, which leads to a new model: the hysteretic autoregressive model. The proposed model enjoys the piecewise linear structure of a threshold model but has a more flexible regime switching mechanism. A sufficient condition is given for geometric ergodicity. Conditional least squares estimation is discussed, and the asymptotic distributions of its estimators and information criteria for model selection are derived. Simulation results and an example support the model.

Suggested Citation

  • Guodong Li & Bo Guan & Wai Keung Li & Philip L. H. Yu, 2015. "Hysteretic autoregressive time series models," Biometrika, Biometrika Trust, vol. 102(3), pages 717-723.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:717-723.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv017
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    References listed on IDEAS

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    1. Pérez-Alonso Alicia & Di Sanzo Silvestro, 2010. "Unemployment and Hysteresis: A Nonlinear Unobserved Components Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-29, December.
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    Cited by:

    1. Ziyi Zhang & Wai Keung Li, 2019. "An Experiment on Autoregressive and Threshold Autoregressive Models with Non-Gaussian Error with Application to Realized Volatility," Economies, MDPI, vol. 7(2), pages 1-11, June.
    2. Cathy W. S. Chen & Sangyeol Lee & K. Khamthong, 2021. "Bayesian inference of nonlinear hysteretic integer-valued GARCH models for disease counts," Computational Statistics, Springer, vol. 36(1), pages 261-281, March.
    3. Guodong Li & Qianqian Zhu & Zhao Liu & Wai Keung Li, 2017. "On Mixture Double Autoregressive Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 306-317, April.
    4. Wei, Honglei & Zhang, Hongfan & Jiang, Hui & Huang, Lei, 2022. "On the semi-varying coefficient dynamic panel data model with autocorrelated errors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    5. Ke Zhu & Wai Keung Li & Philip L. H. Yu, 2017. "Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 528-542, October.
    6. Cathy W. S. Chen & Hong Than-Thi & Manabu Asai, 2021. "On a Bivariate Hysteretic AR-GARCH Model with Conditional Asymmetry in Correlations," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 413-433, August.
    7. Cathy W. S. Chen & Edward M. H. Lin & Tara F. J. Huang, 2022. "Bayesian quantile forecasting via the realized hysteretic GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(7), pages 1317-1337, November.
    8. Karl-Heinz Schild & Karsten Schweikert, 2019. "On the Validity of Tests for Asymmetry in Residual-Based Threshold Cointegration Models," Econometrics, MDPI, vol. 7(1), pages 1-13, March.
    9. Belarbi, Yacine & Hamdi, Fayçal & Khalfi, Abderaouf & Souam, Saïd, 2021. "Growth, institutions and oil dependence: A buffered threshold panel approach," Economic Modelling, Elsevier, vol. 99(C).
    10. Mengya Liu & Qi Li & Fukang Zhu, 2020. "Self-excited hysteretic negative binomial autoregression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 385-415, September.

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