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

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  • Paraschiv, Florentina
  • Bunn, Derek
  • Westgaard, Sjur

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.

Suggested Citation

  • Paraschiv, Florentina & Bunn, Derek & Westgaard, Sjur, 2016. "Estimation and Application of Fully Parametric Multifactor Quantile Regression with Dynamic Coefficients," Working Papers on Finance 1607, University of St. Gallen, School of Finance.
    • Handle: RePEc:usg:sfwpfi:2016:07
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    File URL: http://ux-tauri.unisg.ch/RePEc/usg/sfwpfi/WPF-1607.pdf
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    References listed on IDEAS

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    1. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    2. Gerlach, Richard H. & Chen, Cathy W. S. & Chan, Nancy Y. C., 2011. "Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 481-492.
    3. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian density forecasting of intraday electricity prices using multivariate skew t distributions," International Journal of Forecasting, Elsevier, vol. 24(4), pages 710-727.
    4. Paraschiv, Florentina & Erni, David & Pietsch, Ralf, 2014. "The impact of renewable energies on EEX day-ahead electricity prices," Energy Policy, Elsevier, vol. 73(C), pages 196-210.
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    Citations

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    Cited by:

    1. Nowotarski, Jakub & Weron, Rafał, 2018. "Recent advances in electricity price forecasting: A review of probabilistic forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1548-1568.
    2. Georg Wolff & Stefan Feuerriegel, 2019. "Emissions Trading System of the European Union: Emission Allowances and EPEX Electricity Prices in Phase III," Energies, MDPI, vol. 12(15), pages 1-15, July.
    3. Li, Wei & Paraschiv, Florentina, 2022. "Modelling the evolution of wind and solar power infeed forecasts," Journal of Commodity Markets, Elsevier, vol. 25(C).
    4. Florentina Paraschiv & Dima Mohamad, 2020. "The Nuclear Power Dilemma—Between Perception and Reality," Energies, MDPI, vol. 13(22), pages 1-19, November.
    5. Westgaard, Sjur & Fleten, Stein-Erik & Negash, Ahlmahz & Botterud, Audun & Bogaard, Katinka & Verling, Trude Haugsvaer, 2021. "Performing price scenario analysis and stress testing using quantile regression: A case study of the Californian electricity market," Energy, Elsevier, vol. 214(C).
    6. Rüdiger Kiesel & Florentina Paraschiv & Audun Sætherø, 2019. "On the construction of hourly price forward curves for electricity prices," Computational Management Science, Springer, vol. 16(1), pages 345-369, February.
    7. Sapio, Alessandro, 2019. "Greener, more integrated, and less volatile? A quantile regression analysis of Italian wholesale electricity prices," Energy Policy, Elsevier, vol. 126(C), pages 452-469.
    8. Peter Leoni & Pieter Segaert & Sven Serneels & Tim Verdonck, 2018. "Multivariate constrained robust M‐regression for shaping forward curves in electricity markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(11), pages 1391-1406, November.
    9. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

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    More about this item

    Keywords

    Quantile Regression; Dynamic Coefficients; Parametric Estimation; Elec- tricity Prices;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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