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Functional data analysis of generalized quantile regressions

Author

Listed:
  • Guo, Mengmeng
  • Zhou, Lhan
  • Huang, Jianhua Z.
  • Härdle, Wolfgang Karl

Abstract

Generalized quantile regressions, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We develop a functional data analysis approach to jointly estimate a family of generalized quantile regressions. Our approach assumes that the generalized quantile regressions share some common features that can be summarized by a small number of principal component functions. The principal component functions are modeled as splines and are estimated by minimizing a penalized asymmetric loss measure. An iterative least asymmetrically weighted squares algorithm is developed for computation. While separate estimation of individual generalized quantile regressions usually suffers from large variability due to lack of suffcient data, by borrowing strength across data sets, our joint estimation approach signifcantly improves the estimation effciency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations. These curves are needed to adjust temperature risk factors so that gaussianity is achieved. The normal distribution of temperature variations is vital for pricing weather derivatives with tools from mathematical finance.

Suggested Citation

  • Guo, Mengmeng & Zhou, Lhan & Huang, Jianhua Z. & Härdle, Wolfgang Karl, 2013. "Functional data analysis of generalized quantile regressions," SFB 649 Discussion Papers 2013-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2013-001
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    References listed on IDEAS

    as
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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