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Functional Data Analysis of Generalized Quantile Regressions

Author

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

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

  • Mengmeng Guo & Lhan Zhou & Jianhua Z. Huang & Wolfgang Karl Härdle, 2013. "Functional Data Analysis of Generalized Quantile Regressions," SFB 649 Discussion Papers SFB649DP2013-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2013-001
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    References listed on IDEAS

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    8. Wolfgang Karl Härdle & Brenda López Cabrera, 2012. "The Implied Market Price of Weather Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 59-95, February.
    9. Zografia Anastasiadou & BrendaLópez-Cabrera, 2012. "Statistical Modelling of Temperature Risk," SFB 649 Discussion Papers SFB649DP2012-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    Cited by:

    1. Brenda López Cabrera & Franziska Schulz, 2017. "Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 127-136, January.
    2. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    3. Alona Zharova & Andrija Mihoci & Wolfgang Karl Härdle, 2016. "Academic Ranking Scales in Economics: Prediction and Imputation," SFB 649 Discussion Papers SFB649DP2016-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. T. Górecki & Ł. Smaga, 2017. "Multivariate analysis of variance for functional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2172-2189, September.

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    More about this item

    Keywords

    Asymmetric loss function; Common structure; Functional data analysis; Generalized quantile curve; Iteratively reweighted least squares; Penalization;
    All these keywords.

    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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