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Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model

Author

Listed:
  • Muhammad Jaffri Mohd Nasir

    (Universiti Malaysia Kelantan)

  • Ramzan Nazim Khan

    (The University of Western Australia)

  • Gopalan Nair

    (The University of Western Australia)

  • Darfiana Nur

    (The University of Western Australia)

Abstract

Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the self-exciting threshold autoregressive model, and a group least angle regression (gLAR) algorithm has been applied to obtain an approximate solution to the optimization problem. Although gLAR algorithm is computationally fast, it has been reported that the algorithm tends to estimate too many irrelevant thresholds along with the relevant ones. This paper develops an active-set based block coordinate descent (aBCD) algorithm as an exact optimization method for gLASSO to improve the performance of estimating relevant thresholds. Methods and strategy for choosing the appropriate values of shrinkage parameter for gLASSO are also discussed. To consistently estimate relevant thresholds from the threshold set obtained by the gLASSO, the backward elimination algorithm (BEA) is utilized. We evaluate numerical efficiency of the proposed algorithms, along with the Single-Line-Search (SLS) and the gLAR algorithms through simulated data and real data sets. Simulation studies show that the SLS and aBCD algorithms have similar performance in estimating thresholds although the latter method is much faster. In addition, the aBCD-BEA can sometimes outperform gLAR-BEA in terms of estimating the correct number of thresholds under certain conditions. The results from case studies have also shown that aBCD-BEA performs better in identifying important thresholds.

Suggested Citation

  • Muhammad Jaffri Mohd Nasir & Ramzan Nazim Khan & Gopalan Nair & Darfiana Nur, 2024. "Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model," Statistical Papers, Springer, vol. 65(5), pages 2973-3006, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01472-7
    DOI: 10.1007/s00362-023-01472-7
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    References listed on IDEAS

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    1. Marcella Niglio & Cosimo Damiano Vitale, 2015. "Threshold Vector Arma Models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 2911-2923, July.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    3. Wai-Sum Chan & Albert Wong & Howell Tong, 2004. "Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 37-61.
    4. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    5. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    6. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    7. Qian, Junhui & Su, Liangjun, 2016. "Shrinkage Estimation Of Regression Models With Multiple Structural Changes," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1376-1433, December.
    8. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    9. 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.
    10. 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.
    11. Ngai Hang Chan & Ching-Kang Ing & Yuanbo Li & Chun Yip Yau, 2017. "Threshold Estimation via Group Orthogonal Greedy Algorithm," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 334-345, April.
    12. Gabriela Ciuperca, 2011. "Estimating nonlinear regression with and without change-points by the LAD method," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 717-743, August.
    13. Hedibert F. Lopes & Esther Salazar, 2006. "Bayesian Model Uncertainty In Smooth Transition Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 99-117, January.
    14. 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.
    15. 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.
    16. 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.
    17. John Geweke & Nobuhiko Terui, 1993. "Bayesian Threshold Autoregressive Models For Nonlinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 441-454, September.
    18. Jiazhu Pan & Qiang Xia & Jinshan Liu, 2017. "Bayesian analysis of multiple thresholds autoregressive model," Computational Statistics, Springer, vol. 32(1), pages 219-237, March.
    19. 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.
    20. 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.
    21. 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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