Estimation and Application of Fully Parametric Multifactor Quantile Regression with Dynamic Coefficients

28 Pages Posted: 4 Mar 2016

See all articles by Florentina Paraschiv

Florentina Paraschiv

Zeppelin University, Chair of Finance; Norwegian University of Science and Technology, Faculty of Economics and Management, NTNU Business School; University of St. Gallen, Institute for Operations Research and Computational Finance

Derek W. Bunn

London Business School

Sjur Westgaard

Norwegian University of Science and Technology (NTNU) - Department of Industrial Economics and Technology

Date Written: March 3, 2016

Abstract

This paper develops and applies a novel estimation procedure for quantile regressions with time-varying coefficients based on a fully parametric, multifactor specification. The algorithm recursively filters the multifactor dynamic coefficients with a Kalman filter and parameters are estimated by maximum likelihood. The likelihood function is built on the Skewed-Laplace assumption. In order to eliminate the non-differentiability of the likelihood function, it is reformulated into a non-linear optimisation problem with constraints. A relaxed problem is obtained by moving the constraints into the objective, which is then solved numerically with the Augmented Lagrangian Method. In the context of an application to electricity prices, the results show the importance of modelling the time-varying features and the explicit multi-factor representation of the latent coefficients is consistent with an intuitive understanding of the complex price formation processes involving fundamentals, policy instruments and participant conduct.

Keywords: Quantile Regression, Dynamic Coefficients, Parametric Estimation, Electricity Prices

JEL Classification: C01, C13, C22

Suggested Citation

Paraschiv, Florentina and Bunn, Derek W. and Westgaard, Sjur, Estimation and Application of Fully Parametric Multifactor Quantile Regression with Dynamic Coefficients (March 3, 2016). University of St. Gallen, School of Finance Research Paper No. 2016/07, Available at SSRN: https://ssrn.com/abstract=2741692

Florentina Paraschiv (Contact Author)

Zeppelin University, Chair of Finance ( email )

Am Seemooser Horn 20
Friedrichshafen, 88045
Germany

Norwegian University of Science and Technology, Faculty of Economics and Management, NTNU Business School ( email )

Klæbuveien 72
Trondheim, NO-7030
Norway

University of St. Gallen, Institute for Operations Research and Computational Finance ( email )

Bodanstrasse 6
St. Gallen, 9000
Switzerland

Derek W. Bunn

London Business School ( email )

Sussex Place
Regent's Park
London NW1 4SA
United Kingdom
0207 000 8000 (Phone)

Sjur Westgaard

Norwegian University of Science and Technology (NTNU) - Department of Industrial Economics and Technology ( email )

NO-7491 Trondheim
Norway

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