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

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JAMES W. TAYLOR DEREK W. BUNN
Abstract

SUMMARY 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.

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Article provided by Taylor and Francis Journals in its journal Journal of Applied Statistics.

Volume (Year): 25 (1998)
Issue (Month): 2 (April)
Pages: 193-206
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Handle: RePEc:taf:japsta:v:25:y:1998:i:2:p:193-206

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January. [Downloadable!] (restricted)
  2. Holden, K & Peel, D A, 1990. "On Testing for Unbiasedness and Efficiency of Forecasts," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 58(2), pages 120-27, June.
  3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  4. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Raffaella Giacomini & Ivana Komunjer, 2003. "Evaluation and Combination of Conditional Quantile Forecasts," Boston College Working Papers in Economics 571, Boston College Department of Economics. [Downloadable!]
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