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Combining forecast quantiles using quantile regression: Investigating the derived weights, estimator bias and imposing constraints

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  • James Taylor
  • Derek Bunn

Abstract

A novel proposal for combining forecast distributions is to use quantile regression to combine quantile estimates. We consider the usefulness of the resultant linear combining weights. If the quantile estimates are unbiased, then there is strong intuitive appeal for omitting the constant and constraining the weights to sum to unity in the quantile regression. However, we show that suppressing the constant renders one of the main attractive features of quantile regression invalid. We establish necessary and sufficient conditions for unbiasedness of a quantile estimate, and show that a combination with zero constant and weights that sum to unity is not necessarily unbiased.

Suggested Citation

  • James Taylor & Derek Bunn, 1998. "Combining forecast quantiles using quantile regression: Investigating the derived weights, estimator bias and imposing constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 193-206.
    • Handle: RePEc:taf:japsta:v:25:y:1998:i:2:p:193-206
    DOI: 10.1080/02664769823188
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    References listed on IDEAS

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    Cited by:

    1. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    2. de Menezes, Lilian M. & W. Bunn, Derek & Taylor, James W., 2000. "Review of guidelines for the use of combined forecasts," European Journal of Operational Research, Elsevier, vol. 120(1), pages 190-204, January.
    3. Zongwu Cai & Chaoqun Ma & Xianhua Mi, 2020. "Realized Volatility Forecasting Based on Dynamic Quantile Model Averaging," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202016, University of Kansas, Department of Economics, revised Sep 2020.
    4. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2018. "Quantile forecast combination using stochastic dominance," Empirical Economics, Springer, vol. 55(4), pages 1717-1755, December.
    5. Ewa Ratuszny, 2015. "Risk Modeling of Commodities using CAViaR Models, the Encompassing Method and the Combined Forecasts," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 15, pages 129-156.
    6. Taylor, James W., 2020. "Forecast combinations for value at risk and expected shortfall," International Journal of Forecasting, Elsevier, vol. 36(2), pages 428-441.
    7. Derek Bunn, Arne Andresen, Dipeng Chen, Sjur Westgaard, 2016. "Analysis and Forecasting of Electricty Price Risks with Quantile Factor Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    8. Antonio Bello & Derek Bunn & Javier Reneses & Antonio Muñoz, 2016. "Parametric Density Recalibration of a Fundamental Market Model to Forecast Electricity Prices," Energies, MDPI, vol. 9(11), pages 1-15, November.

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