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Functional Data Analysis of Generalized Quantile Regressions

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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.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-001.

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Length: 26 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2013-001

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Related research

Keywords: Asymmetric loss function; Common structure; Functional data analysis; Generalized quantile curve; Iteratively reweighted least squares; Penalization;

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References

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  1. Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series, Center for Financial Studies (CFS) 2004/10, Center for Financial Studies (CFS).
  2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521785167.
  3. Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(4), pages 819-47, July.
  5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
  6. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 231-252, Spring.
  7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521780506.
  8. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, Biometrika Trust, vol. 95(3), pages 601-619.
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Cited by:
  1. Poeschel, Friedrich, 2012. "Assortative matching through signals," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century, Verein für Socialpolitik / German Economic Association 62061, Verein für Socialpolitik / German Economic Association.

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