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Likelihood-based scoring rules for comparing density forecasts in tails

Author

Listed:
  • Cees Diks

    () (ASE - Amsterdam School of Economics - UvA - University of Amsterdam [Amsterdam])

  • Valentyn Panchenko

    () (Faculty of Business - University of New South Wales [Sydney])

  • Dick Van Dijk

    () (Erasmus University Rotterdam - Erasmus University Rotterdam)

Abstract

We propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. These scoring rules can be interpreted in terms of Kullback-Leibler divergence between weighted versions of the density forecast and the true density. Existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased towards such densities. Using our novel likelihood-based scoring rules avoids this problem.

Suggested Citation

  • Cees Diks & Valentyn Panchenko & Dick Van Dijk, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Post-Print hal-00834423, HAL.
  • Handle: RePEc:hal:journl:hal-00834423 DOI: 10.1016/j.jeconom.2011.04.001 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00834423
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    Cited by:

    1. Shaun P Vahey & Elizabeth C Wakerly, 2013. "Moving towards probability forecasting," BIS Papers chapters,in: Bank for International Settlements (ed.), Globalisation and inflation dynamics in Asia and the Pacific, volume 70, pages 3-8 Bank for International Settlements.
    2. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, Elsevier.
    3. Anne Opschoor & Dick van Dijk & Michel van der Wel, 2014. "Improving Density Forecasts and Value-at-Risk Estimates by Combining Densities," Tinbergen Institute Discussion Papers 14-090/III, Tinbergen Institute.
    4. Barbara Rossi & Tatevik Sekhposyan, 2014. "Alternative tests for correct specification of conditional predictive densities," Economics Working Papers 1416, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2017.
    5. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, pages 3-17.
    6. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    7. Chris McDonald & Craig Thamotheram & Shaun P. Vahey & Elizabeth C. Wakerly, 2016. "Assessing the economic value of probabilistic forecasts in the presence of an inflation target," Reserve Bank of New Zealand Discussion Paper Series DP2016/10, Reserve Bank of New Zealand.
    8. Rossi, Barbara & Sekhposyan, Tatevik, 2013. "Conditional predictive density evaluation in the presence of instabilities," Journal of Econometrics, Elsevier, vol. 177(2), pages 199-212.
    9. Rossi, Barbara & Sekhposyan, Tatevik, 2014. "Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set," International Journal of Forecasting, Elsevier, vol. 30(3), pages 662-682.
    10. Delatola, E.-I. & Griffin, J.E., 2013. "A Bayesian semiparametric model for volatility with a leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 97-110.
    11. McDonald, Christopher & Thamotheram, Craig & Vahey, Shaun P. & Wakerly, Elizabeth C., 2015. "Assessing the Economic Value of Probabilistic Forecasts in the Presence of an Inflation Target," EMF Research Papers 09, Economic Modelling and Forecasting Group.
    12. Tsyplakov, Alexander, 2014. "Theoretical guidelines for a partially informed forecast examiner," MPRA Paper 55017, University Library of Munich, Germany.
    13. Kapetanios, G. & Mitchell, J. & Price, S. & Fawcett, N., 2015. "Generalised density forecast combinations," Journal of Econometrics, Elsevier, vol. 188(1), pages 150-165.
    14. Götz Thomas B. & Hecq Alain & Urbain Jean-Pierre, 2012. "Real-Time Forecast Density Combinations (Forecasting US GDP Growth Using Mixed-Frequency Data)," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. repec:syb:wpbsba:01/2013 is not listed on IDEAS
    16. Raffaella Giacomini & Barbara Rossi, 2015. "Forecasting in Nonstationary Environments: What Works and What Doesn't in Reduced-Form and Structural Models," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 207-229, August.
    17. Cees Diks & Valentyn Panchenko & Oleg Sokolinskiy, & Dick van Dijk, 2013. "Comparing the Accuracy of Copula-Based Multivariate Density Forecasts in Selected Regions of Support," Tinbergen Institute Discussion Papers 13-061/III, Tinbergen Institute.
    18. Lukasz Gatarek & Lennart Hoogerheide & Koen Hooning & Herman K. van Dijk, 2013. "Censored Posterior and Predictive Likelihood in Left-Tail Prediction for Accurate Value at Risk Estimation," Tinbergen Institute Discussion Papers 13-060/III, Tinbergen Institute, revised 06 Mar 2014.
    19. repec:eee:intfor:v:33:y:2017:i:3:p:707-728 is not listed on IDEAS
    20. Gaglianone, Wagner Piazza & Marins, Jaqueline Terra Moura, 2017. "Evaluation of exchange rate point and density forecasts: An application to Brazil," International Journal of Forecasting, Elsevier, vol. 33(3), pages 707-728.
    21. Anufriev, Mikhail & Panchenko, Valentyn, 2015. "Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 241-255.
    22. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, Elsevier.

    More about this item

    Keywords

    C12; C22; C52; C53; Density forecast evaluation; Scoring rules; Weighted likelihood ratio scores; Conditional likelihood; Censored likelihood; Risk management;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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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