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Parameter regimes in partial functional panel regression

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  • Liebl, Dominik
  • Walders, Fabian

Abstract

A new partial functional linear regression model for panel data with time varying parameters is introduced. The parameter vector of the multivariate model component is allowed to be completely time varying while the function-valued parameter of the functional model component is assumed to change over K unknown parameter regimes. Consistency is derived for the suggested estimators and for the classification procedure used to detect the K unknown parameter regimes. Additionally, the convergence rates of the estimators are derived under a double asymptotic differentiating between asymptotic scenarios depending on the relative order of the panel dimensions n and T. The statistical model is motivated by a real data application considering the so-called “idiosyncratic volatility puzzle” using high frequency data from the S&P500.

Suggested Citation

  • Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    • Handle: RePEc:eee:ecosta:v:11:y:2019:i:c:p:105-115
    DOI: 10.1016/j.ecosta.2018.05.003
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    1. Ding, Hui & Liu, Yanghui & Xu, Wenchao & Zhang, Riquan, 2017. "A class of functional partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 68-82.
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    4. Zhou, Jianjun & Chen, Min, 2012. "Spline estimators for semi-functional linear model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 505-513.
    5. Ying Lu & Jiang Du & Zhimeng Sun, 2014. "Functional partially linear quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 317-332, February.
    6. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    7. Ghiglietti, Andrea & Paganoni, Anna Maria, 2017. "Exact tests for the means of Gaussian stochastic processes," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 102-107.
    8. Herskovic, Bernard & Kelly, Bryan & Lustig, Hanno & Van Nieuwerburgh, Stijn, 2016. "The common factor in idiosyncratic volatility: Quantitative asset pricing implications," Journal of Financial Economics, Elsevier, vol. 119(2), pages 249-283.
    9. Shin, Hyejin & Lee, Myung Hee, 2012. "On prediction rate in partial functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 93-106, January.
    10. Fama, Eugene F & French, Kenneth R, 1995. "Size and Book-to-Market Factors in Earnings and Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 131-155, March.
    11. Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    12. Horváth, Lajos & Reeder, Ron, 2012. "Detecting changes in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 310-334.
    13. Hyunphil Choi & Matthew Reimherr, 2018. "A geometric approach to confidence regions and bands for functional parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 239-260, January.
    14. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    15. Heng Lian, 2011. "Functional partial linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 115-128.
    16. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross‐Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, February.
    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. Matthew Schipper & Jeremy M. G. Taylor & Xihong Lin, 2008. "Generalized monotonic functional mixed models with application to modelling normal tissue complications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 149-163, April.
    19. Daowen Zhang & Xihong Lin & MaryFran Sowers, 2007. "Two-Stage Functional Mixed Models for Evaluating the Effect of Longitudinal Covariate Profiles on a Scalar Outcome," Biometrics, The International Biometric Society, vol. 63(2), pages 351-362, June.
    20. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    21. Michael Vogt & Oliver Linton, 2017. "Classification of non-parametric regression functions in longitudinal data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 5-27, January.
    22. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    23. Hou, Kewei & Loh, Roger K., 2016. "Have we solved the idiosyncratic volatility puzzle?," Journal of Financial Economics, Elsevier, vol. 121(1), pages 167-194.
    24. Germán Aneiros-Pérez & Philippe Vieu, 2013. "Testing linearity in semi-parametric functional data analysis," Computational Statistics, Springer, vol. 28(2), pages 413-434, April.
    25. Fu, Fangjian, 2009. "Idiosyncratic risk and the cross-section of expected stock returns," Journal of Financial Economics, Elsevier, vol. 91(1), pages 24-37, January.
    26. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
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