Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/79585
Authors: 
Guo, Mengmeng
Zhou, Lhan
Huang, Jianhua Z.
Härdle, Wolfgang Karl
Year of Publication: 
2013
Series/Report no.: 
SFB 649 Discussion Paper 2013-001
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.
Subjects: 
asymmetric loss function
common structure
functional data analysis
generalized quantile curve
iteratively reweighted least squares
penalization
JEL: 
C13
C23
C38
Q54
Document Type: 
Working Paper

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