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Threshold Variable Selection In Open‐Loop Threshold Autoregressive Models

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  • Rong Chen

Abstract

. An open‐loop threshold autoregressive model is defined as The main difficulty for building such a model is that the threshold variable Zt is usually unknown. In practice, there may exist many possible candidates for the threshold variable Zt. It is difficult and tedious, if not impossible, to search for the best among all the candidates using standard model selection procedures. In this paper, we introduce a digression concept and propose two simple algorithms to classify the observations without knowing the threshold variable. The classification is then used with several graphical procedures to search for the most suitable threshold variable. Simulated and real examples are included to illustrate the proposed procedures.

Suggested Citation

  • Rong Chen, 1995. "Threshold Variable Selection In Open‐Loop Threshold Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 461-481, September.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:5:p:461-481
    DOI: 10.1111/j.1467-9892.1995.tb00247.x
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    Cited by:

    1. Liu, Xialu & Chen, Rong, 2020. "Threshold factor models for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 53-70.
    2. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    3. Laurent Ferrara & Dominique Guégan, 2006. "Detection of the Industrial Business Cycle using SETAR Models," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2005(3), pages 353-371.
    4. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, September.
    6. Colin Lizieri & Steven Satchell & Elaine Worzala & Roberto Dacco', 1998. "Real Interest Regimes and Real Estate Performance: A Comparison of U.K. and U.S. Markets," Journal of Real Estate Research, Taylor & Francis Journals, vol. 16(3), pages 339-356, January.
    7. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
    8. Franses, Philip Hans & Paap, Richard & Vroomen, Bjorn, 2004. "Forecasting unemployment using an autoregression with censored latent effects parameters," International Journal of Forecasting, Elsevier, vol. 20(2), pages 255-271.
    9. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521817707.
    10. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    11. Franses, Ph.H.B.F. & Paap, R., 1998. "Censored latent effects autoregression, with an application to US unemployment," Econometric Institute Research Papers EI 9841, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Mayte Suarez -Farinas & Carlos E. Pedreira & Marcelo C. Medeiros, 2004. "Local Global Neural Networks: A New Approach for Nonlinear Time Series Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1092-1107, December.
    13. Cathy Chen & Feng-Chi Liu & Mike So, 2013. "Threshold variable selection of asymmetric stochastic volatility models," Computational Statistics, Springer, vol. 28(6), pages 2415-2447, December.
    14. Xialu Liu & Elynn Y. Chen, 2022. "Identification and estimation of threshold matrix‐variate factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1383-1417, September.
    15. Ip, Wai-Cheung & Wong, Heung & Li, Yuan & Xie, Zhongjie, 1999. "Threshold variable selection by wavelets in open-loop threshold autoregressive models," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 375-392, May.
    16. Franses, Ph.H.B.F. & Paap, R., 1998. "Modelling asymmetric persistence over the business cycle," Econometric Institute Research Papers EI 9852, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. De Gooijer, Jan G. & Ray, Bonnie K., 2003. "Modeling vector nonlinear time series using POLYMARS," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 73-90, February.

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