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Comparing Density Forecasts via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods

  • Raffaella Giacomini


    (Boston College)

This paper proposes tests for comparing the accuracy of density forecasts. The evaluation makes use of scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. In particular, a logarithmic scoring rule leads to the development of asymptotic and bootstrap 'weighted likelihood ratio' tests. I conclude with an application to S&P500 daily returns, comparing the performance of density forecasts obtained from GARCH models with different distributional assumptions.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 583.

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Date of creation: 01 Jun 2002
Date of revision:
Handle: RePEc:boc:bocoec:583
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  1. Lopez, Jose A, 2001. "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 87-109, March.
  2. Peter F. Christoffersen & Francis X. Diebold, 1997. "Optimal prediction under asymmetric loss," Working Papers 97-11, Federal Reserve Bank of Philadelphia.
  3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  4. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc.
  5. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
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