Functional Data Analysis of Generalized Quantile Regressions
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.
|Date of creation:||Jan 2013|
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- Wolfgang Härdle & Brenda López Cabrera, 2009. "Implied Market Price of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- repec:cup:cbooks:9780521785167 is not listed on IDEAS
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"Weather Forecasting for Weather Derivatives,"
NBER Working Papers
10141, National Bureau of Economic Research, Inc.
- Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series 2004/10, Center for Financial Studies (CFS).
- Sean D. Campbell & Francis X. Diebold, 2002. "Weather Forecasting for Weather Derivatives," Center for Financial Institutions Working Papers 02-42, Wharton School Center for Financial Institutions, University of Pennsylvania.
- repec:cup:cbooks:9780521780506 is not listed on IDEAS
- 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.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
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