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A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting

Author

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  • Li, Yushu

    () (Dept. of Business and Management Science, Norwegian School of Economics)

  • Andersson, Jonas

    () (Dept. of Business and Management Science, Norwegian School of Economics)

Abstract

In this paper, we propose a likelihood ratio and Markov chain based method to evaluate density forecasting. This method can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. This method is an extension of the widely applied evaluation method for interval forecasting proposed by Christoffersen (1998). It is also a more refined approach than the pure contingency table based density forecasting method in Wallis (2003). We show that our method has very high power against incorrect forecasting distributions and dependence. Moreover, the straightforwardness and ease of application of this joint test provide a high potentiality for further applications in both financial and economical areas.

Suggested Citation

  • Li, Yushu & Andersson, Jonas, 2014. "A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting," Discussion Papers 2014/12, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2014_012
    as

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    File URL: http://hdl.handle.net/11250/194978
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    References listed on IDEAS

    as
    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    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. 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.
    4. Tae-Hwy Lee & Yong Bao & Burak Saltoğlu, 2007. "Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003;," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 203-225.
    5. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    6. 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.
    7. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    8. 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.
    9. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    10. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    11. 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.
    12. 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.
    13. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    14. Elena‐Ivona Dumitrescu & Christophe Hurlin & Jaouad Madkour, 2013. "Testing Interval Forecasts: A GMM‐Based Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(2), pages 97-110, March.
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    More about this item

    Keywords

    Likelihood ratio test; Markov Chain; Density forecasting;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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