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Functional index coefficient models with variable selection

Author

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  • Cai, Zongwu
  • Juhl, Ted
  • Yang, Bingduo

Abstract

We consider model (variable) selection in a semi-parametric time series model with functional coefficients. Variable selection in the semi-parametric model must account for the fact that the parametric part of the model is estimated at a faster convergence rate than the nonparametric component. Our variable selection procedures employ a smoothly clipped absolute deviation penalty function and consist of two steps. The first is to select covariates with functional coefficients that enter in the semi-parametric model. Then, we perform variable selection for variables with parametric coefficients. The asymptotic properties, such as consistency, sparsity and the oracle property of these two-step estimators are established. A Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed estimators and variable selection procedures. Finally, an empirical example exploring the predictability of asset returns demonstrates the practical application of the proposed functional index coefficient autoregressive models and variable selection procedures.

Suggested Citation

  • Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
  • Handle: RePEc:eee:econom:v:189:y:2015:i:2:p:272-284
    DOI: 10.1016/j.jeconom.2015.03.022
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    Cited by:

    1. Bingduo Yang & Christian M. Hafner & Guannan Liu & Wei Long, 2021. "Semiparametric estimation and variable selection for single‐index copula models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 962-988, November.
    2. Zhao, Weihua & Lian, Heng, 2017. "Quantile index coefficient model with variable selection," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 40-58.
    3. Bingduo Yang & Zongwu Cai & Christian M. Hafner & Guannan Liu, 2018. "Trending Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201809, University of Kansas, Department of Economics, revised Sep 2018.
    4. Ling, Shiqing & McAleer, Michael & Tong, Howell, 2015. "Frontiers in Time Series and Financial Econometrics: An overview," Journal of Econometrics, Elsevier, vol. 189(2), pages 245-250.
    5. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Series estimation for single-index models under constraints," Monash Econometrics and Business Statistics Working Papers 5/18, Monash University, Department of Econometrics and Business Statistics.
    6. Chaohua Dong & Jiti Gao & Bin Peng, 2016. "Another Look at Single-Index Models Based on Series Estimation," Monash Econometrics and Business Statistics Working Papers 19/16, Monash University, Department of Econometrics and Business Statistics.
    7. repec:kan:wpaper:202105 is not listed on IDEAS
    8. Bin Chen & Kenwin Maung, 2020. "Time-varying Forecast Combination for High-Dimensional Data," Papers 2010.10435, arXiv.org.
    9. Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    10. Liu, Yanghui & Li, Yehua & Carroll, Raymond J. & Wang, Naisyin, 2022. "Predictive functional linear models with diverging number of semiparametric single-index interactions," Journal of Econometrics, Elsevier, vol. 230(2), pages 221-239.
    11. Ling, S. & McAleer, M.J. & Tong, H., 2015. "Frontiers in Time Series and Financial Econometrics," Econometric Institute Research Papers EI 2015-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Zhao, Weihua & Zhou, Yan & Lian, Heng, 2018. "Time-varying quantile single-index model for multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 32-49.

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    More about this item

    Keywords

    Functional index coefficient autoregressive model; Model selection; Oracle property; Penalty function; Smoothly clipped absolute deviation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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