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LASSO estimation of threshold autoregressive models

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  • Chan, Ngai Hang
  • Yau, Chun Yip
  • Zhang, Rong-Mao

Abstract

This paper develops a novel approach for estimating a threshold autoregressive (TAR) model with multiple-regimes and establishes its large sample properties. By reframing the problem in a regression variable selection context, a least absolute shrinkage and selection operator (LASSO) procedure is proposed to estimate a TAR model with an unknown number of thresholds, where the computation can be performed efficiently. It is further shown that the number and the location of the thresholds can be consistently estimated. A near optimal convergence rate of the threshold parameters is also established. Simulation studies are conducted to assess the performance in finite samples. The results are illustrated with an application to the quarterly US real GNP data over the period 1947–2009.

Suggested Citation

  • Chan, Ngai Hang & Yau, Chun Yip & Zhang, Rong-Mao, 2015. "LASSO estimation of threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 285-296.
    • Handle: RePEc:eee:econom:v:189:y:2015:i:2:p:285-296
    DOI: 10.1016/j.jeconom.2015.03.023
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    References listed on IDEAS

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    1. Harchaoui, Z. & Lévy-Leduc, C., 2010. "Multiple Change-Point Estimation With a Total Variation Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1480-1493.
    2. Coakley, Jerry & Fuertes, Ana-Maria & Perez, Maria-Teresa, 2003. "Numerical issues in threshold autoregressive modeling of time series," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2219-2242, September.
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    5. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
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    7. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    8. Ngai Hang Chan & Chun Yip Yau & Rong-Mao Zhang, 2014. "Group LASSO for Structural Break Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 590-599, June.
    9. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

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    4. Chih‐Hao Chang & Kam‐Fai Wong & Wei‐Yee Lim, 2023. "Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 4-47, February.
    5. Fan, Jianqing & Gong, Wenyan & Zhu, Ziwei, 2019. "Generalized high-dimensional trace regression via nuclear norm regularization," Journal of Econometrics, Elsevier, vol. 212(1), pages 177-202.
    6. Verdejo, Humberto & Awerkin, Almendra & Becker, Cristhian & Olguin, Gabriel, 2017. "Statistic linear parametric techniques for residential electric energy demand forecasting. A review and an implementation to Chile," Renewable and Sustainable Energy Reviews, Elsevier, vol. 74(C), pages 512-521.
    7. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    8. Ma, Chenchen & Tu, Yundong, 2023. "Shrinkage estimation of multiple threshold factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1876-1892.
    9. Ma, Chenchen & Tu, Yundong, 2023. "Group fused Lasso for large factor models with multiple structural breaks," Journal of Econometrics, Elsevier, vol. 233(1), pages 132-154.

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    More about this item

    Keywords

    Group lasso; Information criterion; Least angle regression (LARS); Multiple regimes;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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