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Theoretical guidelines for a partially informed forecast examiner

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  • Tsyplakov, Alexander

Abstract

The paper explores probability theory foundations behind evaluation of probabilistic forecasts. The emphasis is on a situation when the forecast examiner possesses only partially the information which was available and was used to produce a forecast. We argue that in such a situation forecasts should be judged by their conditional auto-calibration. Necessary and sufficient conditions of auto-calibration are discussed and expressed in the form of testable moment conditions. The paper also analyzes relationships between forecast calibration and forecast efficiency.

Suggested Citation

  • Tsyplakov, Alexander, 2014. "Theoretical guidelines for a partially informed forecast examiner," MPRA Paper 55017, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:55017
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    File URL: https://mpra.ub.uni-muenchen.de/55017/1/MPRA_paper_55017.pdf
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    File URL: https://mpra.ub.uni-muenchen.de/67333/1/MPRA_paper_67333.pdf
    File Function: revised version
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    References listed on IDEAS

    as
    1. Engelberg, Joseph & Manski, Charles F. & Williams, Jared, 2009. "Comparing the Point Predictions and Subjective Probability Distributions of Professional Forecasters," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 30-41.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    4. Galbraith, John W. & van Norden, Simon, 2011. "Kernel-based calibration diagnostics for recession and inflation probability forecasts," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1041-1057, October.
    5. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (US).
    6. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F., 2011. "Scoring rules and survey density forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 379-393.
    7. Wallis, Kenneth F., 2003. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 165-175.
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    10. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    11. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    12. Diebold, Francis X & Rudebusch, Glenn D, 1989. "Scoring the Leading Indicators," The Journal of Business, University of Chicago Press, vol. 62(3), pages 369-391, July.
    13. Giorgio Valente & Lucio Sarno, 2004. "Comparing the accuracy of density forecasts from competing models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(8), pages 541-557.
    14. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    15. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    16. Michael P. Clements & David I. Harvey, 2010. "Forecast encompassing tests and probability forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 1028-1062.
    17. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268.
    18. Yi‐Ting Chen, 2011. "Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 409-450, July.
    19. James Mitchell & Kenneth F. Wallis, 2011. "Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 1023-1040, September.
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    22. Tsyplakov, Alexander, 2011. "Evaluating density forecasts: a comment," MPRA Paper 31184, University Library of Munich, Germany.
    23. repec:hal:journl:peer-00834423 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    2. Ziegel, Johanna F. & Krueger, Fabian & Jordan, Alexander & Fasciati, Fernando, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Working Papers 0632, University of Heidelberg, Department of Economics.
    3. Werner Ehm & Tilmann Gneiting & Alexander Jordan & Fabian Krüger, 2016. "Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 505-562, June.
    4. Johanna F. Ziegel & Fabian Kruger & Alexander Jordan & Fernando Fasciati, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Papers 1705.04537, arXiv.org.

    More about this item

    Keywords

    probabilistic forecast; forecast calibration; moment condition; probability integral transform; orthogonality condition; scoring rule; forecast encompassing;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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