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

  • James Taylor
  • Derek Bunn
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    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 & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 25 (1998)
    Issue (Month): 2 ()
    Pages: 193-206

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    Handle: RePEc:taf:japsta:v:25:y:1998:i:2:p:193-206
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    1. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    2. Robert T. Clemen & Robert L. Winkler, 1993. "Aggregating Point Estimates: A Flexible Modeling Approach," Management Science, INFORMS, vol. 39(4), pages 501-515, April.
    3. Holden, K & Peel, D A, 1990. "On Testing for Unbiasedness and Efficiency of Forecasts," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(2), pages 120-27, June.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    6. Robert L. Winkler, 1981. "Combining Probability Distributions from Dependent Information Sources," Management Science, INFORMS, vol. 27(4), pages 479-488, April.
    7. 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.
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