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Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks

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  • Chun Yip Yau
  • Chong Man Tang
  • Thomas C. M. Lee

Abstract

The threshold autoregressive (TAR) model is a class of nonlinear time series models that have been widely used in many areas. Due to its nonlinear nature, one major difficulty in fitting a TAR model is the estimation of the thresholds. As a first contribution, this article develops an automatic procedure to estimate the number and values of the thresholds, as well as the corresponding AR order and parameter values in each regime. These parameter estimates are defined as the minimizers of an objective function derived from the minimum description length (MDL) principle. A genetic algorithm (GA) is constructed to efficiently solve the associated minimization problem. The second contribution of this article is the extension of this framework to piecewise TAR modeling; that is, the time series is partitioned into different segments for which each segment can be adequately modeled by a TAR model, while models from adjacent segments are different. For such piecewise TAR modeling, a procedure is developed to estimate the number and locations of the breakpoints, together with all other parameters in each segment. Desirable theoretical results are derived to lend support to the proposed methodology. Simulation experiments and an application to an U.S. GNP data are used to illustrate the empirical performances of the methodology. Supplementary materials for this article are available online.

Suggested Citation

  • Chun Yip Yau & Chong Man Tang & Thomas C. M. Lee, 2015. "Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1175-1186, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:1175-1186
    DOI: 10.1080/01621459.2014.954706
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    References listed on IDEAS

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    1. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    2. 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.
    3. Thomas C. M. Lee, 2001. "An Introduction to Coding Theory and the Two‐Part Minimum Description Length Principle," International Statistical Review, International Statistical Institute, vol. 69(2), pages 169-183, August.
    4. 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.
    5. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    6. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
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    Cited by:

    1. Victor V. Konev & Sergey E. Vorobeychikov, 2022. "Fixed accuracy estimation of parameters in a threshold autoregressive model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 685-711, August.
    2. Varun Agiwal & Jitendra Kumar, 2020. "Bayesian estimation for threshold autoregressive model with multiple structural breaks," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 361-382, December.
    3. Domenico Cucina & Manuel Rizzo & Eugen Ursu, 2018. "Identification of multiregime periodic autotregressive models by genetic algorithms," Post-Print hal-03187870, HAL.
    4. Jeffrey Frankel, 2023. "Estimation of Nonlinear Exchange Rate Dynamics in Evolving Regimes," CID Working Papers 429, Center for International Development at Harvard University.
    5. 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.

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