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Murphy Diagrams: Forecast Evaluation of Expected Shortfall

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  • Ziegel, Johanna F.
  • Krueger, Fabian
  • Jordan, Alexander
  • Fasciati, Fernando

Abstract

Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little intuitive or empirical guidance is currently available, which renders the choice of scoring function awkward in practice. We therefore develop graphical checks (Murphy diagrams) of whether one forecast method dominates another under a relevant class of scoring functions, and propose an associated hypothesis test. We illustrate these tools with simulation examples and an empirical analysis of S&P 500 and DAX returns.

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  • 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.
    • Handle: RePEc:awi:wpaper:0632
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    Cited by:

    1. Sander Barendse & Andrew J. Patton, 2022. "Comparing Predictive Accuracy in the Presence of a Loss Function Shape Parameter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1057-1069, June.
    2. Taylor, James W., 2020. "Forecast combinations for value at risk and expected shortfall," International Journal of Forecasting, Elsevier, vol. 36(2), pages 428-441.

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