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Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach

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  • Jianhua Z. Huang
  • Haipeng Shen

Abstract

We propose a global smoothing method based on polynomial splines for the estimation of functional coefficient regression models for non-linear time series. Consistency and rate of convergence results are given to support the proposed estimation method. Methods for automatic selection of the threshold variable and significant variables (or lags) are discussed. The estimated model is used to produce multi-step-ahead forecasts, including interval forecasts and density forecasts. The methodology is illustrated by simulations and two real data examples. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

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  • Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534.
  • Handle: RePEc:bla:scjsta:v:31:y:2004:i:4:p:515-534
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    1. repec:spr:testjl:v:26:y:2017:i:3:d:10.1007_s11749-017-0525-7 is not listed on IDEAS
    2. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    3. repec:wyi:journl:002135 is not listed on IDEAS
    4. Zongwu Cai, 2013. "Functional Coefficient Models for Economic and Financial Data," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Li, Rui & Wan, Alan T.K. & You, Jinhong, 2016. "Semiparametric GMM estimation and variable selection in dynamic panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 401-423.
    6. Cao, Yanrong & Lin, Haiqun & Wu, Tracy Z. & Yu, Yan, 2010. "Penalized spline estimation for functional coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 891-905, April.
    7. Yang, Guangren & Zhou, Yong, 2014. "Semiparametric varying-coefficient study of mean residual life models," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 226-238.
    8. Yehua Li & Marc G. Genton, 2009. "Single-Index Additive Vector Autoregressive Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 369-388.
    9. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    10. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    11. Kong, Dehan & Bondell, Howard D. & Wu, Yichao, 2015. "Domain selection for the varying coefficient model via local polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 236-250.
    12. Zhou, Jianjun & Chen, Min, 2012. "Spline estimators for semi-functional linear model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 505-513.
    13. repec:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0711-1 is not listed on IDEAS
    14. Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators under Weak Dependence and Weak Conditions," Cowles Foundation Discussion Papers 1976, Cowles Foundation for Research in Economics, Yale University.
    15. Harvill, Jane L. & Ray, Bonnie K., 2006. "Functional coefficient autoregressive models for vector time series," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3547-3566, August.
    16. Qiu, Jia & Li, Degao & You, Jinhong, 2015. "SCAD-penalized regression for varying-coefficient models with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 100-118.
    17. Qing-Yan Peng & Jian-Jun Zhou & Nian-Sheng Tang, 2016. "Varying coefficient partially functional linear regression models," Statistical Papers, Springer, vol. 57(3), pages 827-841, September.
    18. Cizek, Pavel & Koo, Chao, 2017. "Jump-Preserving Varying-Coefficient Models for Nonlinear Time Series," Discussion Paper 2017-017, Tilburg University, Center for Economic Research.
    19. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    20. Farcomeni Alessio & Arima Serena, 2012. "A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-31, June.
    21. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    22. Xiaohong Chen & Timothy M. Christensen, 2014. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," CeMMAP working papers CWP46/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. Yan-Yong Zhao & Jin-Guan Lin & Xing-Fang Huang, 2016. "Nonparametric estimation in generalized varying-coefficient models based on iterative weighted quasi-likelihood method," Computational Statistics, Springer, vol. 31(1), pages 247-268, March.

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