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Evaluating density forecasts

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  • Francis X. Diebold
  • Todd A. Gunther
  • Anthony S. Tay

Abstract

The authors propose methods for evaluating and improving density forecasts. They focus primarily on methods that are applicable regardless of the particular user's loss function, though they take explicit account of the relationships between density forecasts, action choices, and the corresponding expected loss throughout. They illustrate the methods with a detailed series of examples, and they discuss extensions to improving and combining suboptimal density forecasts, multistep-ahead density forecast evaluation, multivariate density forecast evaluation, monitoring for structural change and its relationship to density forecasting, and density forecast evaluation with known loss function.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Philadelphia in its series Working Papers with number 97-6.

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Date of creation: 1997
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Handle: RePEc:fip:fedpwp:97-6

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Keywords: Forecasting;

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References

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  1. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
  2. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  3. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  4. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 1-46 National Bureau of Economic Research, Inc.
  5. Francis X. Diebold & Peter F. Christoffersen, 1997. "Cointegration and Long-Horizon Forecasting," IMF Working Papers 97/61, International Monetary Fund.
  6. Peter F. Christoffersen & Francis X. Diebold, . "Optimal Prediction Under Asymmetric Loss," CARESS Working Papres 97-20, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  7. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  8. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-40, November.
  9. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  10. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  11. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October.
  12. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
  13. 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 841-62, November.
  14. Granger, C.W.J. & Pesaran, H., 1996. "A Decision_Theoretic Approach to Forecast Evaluation," Cambridge Working Papers in Economics 9618, Faculty of Economics, University of Cambridge.
  15. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
  16. Clemen, Robert T. & Murphy, Allan H. & Winkler, Robert L., 1995. "Screening probability forecasts: contrasts between choosing and combining," International Journal of Forecasting, Elsevier, vol. 11(1), pages 133-145, March.
  17. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  18. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
  19. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  20. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  21. Campbell, Bryan & Ghysels, Eric, 1995. "Federal Budget Projections: A Nonparametric Assessment of Bias and Efficiency," The Review of Economics and Statistics, MIT Press, vol. 77(1), pages 17-31, February.
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