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Simultaneous variable selection and structural identification for time‐varying coefficient models

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  • Ngai Hang Chan
  • Linhao Gao
  • Wilfredo Palma

Abstract

Time‐varying coefficient models are important tools in time series analysis due to their flexibility to fit non‐stationary data. To improve the accuracy of these models, it is important to identify covariates with null, constant and time‐varying effects and to estimate their coefficients. This article proposes a combination of the local linear smoothing method and the adaptive group lasso penalty approach to achieve covariate identification and coefficient estimation. The penalty term consists of two parts. The first term penalizes the norm of the coefficient function, which is used to select relevant variables. The second term penalizes the norm of the derivative function, which assesses the constancy of the coefficient functions. The asymptotic properties of the proposed methodology are established. Performance of the proposed method is demonstrated using simulated data along with an application to the analysis of the air quality and health data in Hong Kong.

Suggested Citation

  • Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
  • Handle: RePEc:bla:jtsera:v:43:y:2022:i:4:p:511-531
    DOI: 10.1111/jtsa.12626
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    References listed on IDEAS

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    1. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    2. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    4. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    5. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2018. "Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 88-100, January.
    6. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    7. Marios Sergides & Efstathios Paparoditis, 2008. "Bootstrapping the Local Periodogram of Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 264-299, March.
    8. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    9. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    10. Kenji Sakiyama & Masanobu Taniguchi, 2003. "Testing Composite Hypotheses for Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 483-504, July.
    11. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    12. EICHLER , Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," LIDAM Reprints ISBA 2011013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Eichler, Michael & Motta, Giovanni & von Sachs, Rainer, 2011. "Fitting dynamic factor models to non-stationary time series," Journal of Econometrics, Elsevier, vol. 163(1), pages 51-70, July.
    14. HONDA, Toshio & 本田, 敏雄 & YABE, Ryota & 矢部, 竜太, 2017. "Variable selection and structure identification for varying coefficient Cox models," Discussion Papers 2016-05, Graduate School of Economics, Hitotsubashi University.
    15. Jiti Gao & Kim Hawthorne, 2006. "Semiparametric estimation and testing of the trend of temperature series," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 332-355, July.
    16. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    17. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    18. 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.
    19. Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.
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