Functional Data Analysis of Generalized Quantile Regressions

SFB 649 Discussion Paper 2013-001

26 Pages Posted: 5 Jan 2017

See all articles by Mengmeng Guo

Mengmeng Guo

Southwestern University of Finance and Economics (SWUFE) - Research Institute of Economics & Management

Lhan Zhou

Texas A & M University

Jianhua Huang

Texas A&M University - Department of Statistics

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Date Written: January 2, 2013

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 sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, 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.

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

JEL Classification: C13, C23, C38, Q54

Suggested Citation

Guo, Mengmeng and Zhou, Lhan and Huang, Jianhua and Härdle, Wolfgang K., Functional Data Analysis of Generalized Quantile Regressions (January 2, 2013). SFB 649 Discussion Paper 2013-001, Available at SSRN: https://ssrn.com/abstract=2892652 or http://dx.doi.org/10.2139/ssrn.2892652

Mengmeng Guo

Southwestern University of Finance and Economics (SWUFE) - Research Institute of Economics & Management ( email )

55 Guanghuacun Street
Chengdu, Sichuan 610074
China

Lhan Zhou

Texas A & M University ( email )

2200 Campbell St,
Commerce, TX 75428
United States

Jianhua Huang

Texas A&M University - Department of Statistics ( email )

155 Ireland Street
447 Blocker
College Station, TX 77843
United States

Wolfgang K. Härdle (Contact Author)

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

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