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A likelihood ratio and Markov chain‐based method to evaluate density forecasting

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  • Yushu Li
  • Jonas Andersson
Abstract
In this paper, we propose a likelihood ratio‐based method to evaluate density forecasts, which can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. Unlike the well‐known Berkowitz test, the proposed method does not require a parametric specification of time dynamics. We compare our method with the method proposed by several other tests and show that our methodology has very high power against both dependence and incorrect forecasting distributions. Moreover, the loss of power, caused by the nonparametric nature of the specification of the dynamics, is shown to be small compared to the Berkowitz test, even when the parametric form of dynamics is correctly specified in the latter method.

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  • Yushu Li & Jonas Andersson, 2020. "A likelihood ratio and Markov chain‐based method to evaluate density forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 47-55, January.
    • Handle: RePEc:wly:jforec:v:39:y:2020:i:1:p:47-55
    DOI: 10.1002/for.2604
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    References listed on IDEAS

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    1. 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.
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    3. Michael P. Clements & Nick Taylor, 2003. "Evaluating interval forecasts of high-frequency financial data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 445-456.
    4. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    5. 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.
    6. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    7. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
    8. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    9. 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.
    10. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
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    Cited by:

    1. Yang Wang & Jifa Wang, 2021. "Design of link prediction algorithm for complex network based on the comprehensive influence of predicting nodes and neighbor nodes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 911-920, August.

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