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Efficient evaluation of multidimensional time-varying density forecasts, with applications to risk management

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  • Polanski, Arnold
  • Stoja, Evarist

Abstract

We propose two simple evaluation methods for time-varying density forecasts of continuous higher-dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantages of the second method are not only its applicability to arbitrary continuous distributions, but also the evaluation of the forecast accuracy in specific regions of its domain, as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In both simulations and an empirical study, we examine the performances of the two tests.

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  • Polanski, Arnold & Stoja, Evarist, 2012. "Efficient evaluation of multidimensional time-varying density forecasts, with applications to risk management," International Journal of Forecasting, Elsevier, vol. 28(2), pages 343-352.
  • Handle: RePEc:eee:intfor:v:28:y:2012:i:2:p:343-352
    DOI: 10.1016/j.ijforecast.2010.10.007
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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.
    2. 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 (U.S.).
    3. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    4. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    5. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
    6. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    7. Bai, Jushan & Chen, Zhihong, 2008. "Testing multivariate distributions in GARCH models," Journal of Econometrics, Elsevier, vol. 143(1), pages 19-36, March.
    8. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    9. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    10. Fuchun Li & Greg Tkacz, 2001. "A Consistent Bootstrap Test for Conditional Density Functions with Time-Dependent Data," Staff Working Papers 01-21, Bank of Canada.
    11. Clements, Michael P. & Smith, Jeremy, 2002. "Evaluating multivariate forecast densities: a comparison of two approaches," International Journal of Forecasting, Elsevier, vol. 18(3), pages 397-407.
    12. 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.
    13. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    14. Chen, Bin & Hong, Yongmiao, 2010. "Characteristic Function–Based Testing For Multifactor Continuous-Time Markov Models Via Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1115-1179, August.
    15. Guidolin, Massimo & Timmermann, Allan, 2006. "Term structure of risk under alternative econometric specifications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 285-308.
    16. Hong, Yongmiao & Li, Haitao & Zhao, Feng, 2007. "Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates," Journal of Econometrics, Elsevier, vol. 141(2), pages 736-776, December.
    17. Valentina Corradi & Norman Swanson, 2006. "Predictive Density Evaluation. Revised," Departmental Working Papers 200621, Rutgers University, Department of Economics.
    18. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    19. 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.
    20. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    21. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 5, pages 197-284, Elsevier.
    22. 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.
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    1. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    2. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," Bank of England working papers 660, Bank of England.
    3. Ko, Stanley I.M. & Park, Sung Y., 2013. "Multivariate density forecast evaluation: A modified approach," International Journal of Forecasting, Elsevier, vol. 29(3), pages 431-441.

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