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Nested sub-sample search algorithm for estimation of threshold models

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  • Li, Dong
  • Tong, Howell

Abstract

Threshold models have been popular for modelling nonlinear phenomena in diverse areas, in part due to their simple fitting and often clear model interpretation. A commonly used approach to fit a threshold model is the (conditional) least squares method, for which the standard grid search typically requires O(n) operations for a sample of size n; this is substantial for large n, especially in the context of panel time series. This paper proposes a novel method, the nested sub-sample search algorithm, which reduces the number of least squares operations drastically to O(log n) for large sample size. We demonstrate its speed and reliability via Monte Carlo simulation studies with finite samples. Possible extension to maximum likelihood estimation is indicated.

Suggested Citation

  • Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:68880
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    File URL: http://eprints.lse.ac.uk/68880/
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
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    4. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
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    6. 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.
    7. 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.
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    12. 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.
    13. Hansen Bruce E., 1997. "Inference in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-16, April.
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    Cited by:

    1. Han Li & Kai Yang & Shishun Zhao & Dehui Wang, 2018. "First-order random coefficients integer-valued threshold autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 305-331, July.

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    More about this item

    Keywords

    Least squares estimation; maximum likelihood estimation; nested sub-sample search algorithm; standard grid search algorithm; threshold model;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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