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Evaluating density forecasts

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

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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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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  1. 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.
  2. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  3. 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.
  4. West, K.D. & McCracken, M.W., 1997. "Regression-Based Tests of Predictive Ability," Working papers 9710, Wisconsin Madison - Social Systems.
  5. Peter F. Christoffersen & Francis X. Diebold, 1997. "Cointegration and long-horizon forecasting," Working Papers 97-14, Federal Reserve Bank of Philadelphia.
  6. 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.
  7. Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
  8. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  9. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
  10. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
  11. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  12. 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.).
  13. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  14. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  21. 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.
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