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

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  • Raffaella Giacomini

    ()
    (Boston College)

Abstract

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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Bibliographic Info

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

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Length: 37 pages
Date of creation: 01 Jun 2002
Date of revision:
Handle: RePEc:boc:bocoec:583

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Keywords: density forecasting; scoring rules; predictive ability; forecast comparison;

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  1. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  2. West, K.D., 1994. "Asymptotic Inference About Predictive Ability," Working papers 9417, Wisconsin Madison - Social Systems.
  3. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December.
  4. Jose A. Lopez, 1995. "Evaluating the predictive accuracy of volatility models," Research Paper 9524, Federal Reserve Bank of New York.
  5. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
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Cited by:
  1. Isao Ishida, 2005. "Scanning Multivariate Conditional Densities with Probability Integral Transforms," CIRJE F-Series CIRJE-F-369, CIRJE, Faculty of Economics, University of Tokyo.
  2. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
  3. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228.
  4. Clements, Michael P. & Franses, Philip Hans & Swanson, Norman R., 2004. "Forecasting economic and financial time-series with non-linear models," International Journal of Forecasting, Elsevier, vol. 20(2), pages 169-183.
  5. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
  6. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
  7. Corradi, Valentina & Swanson, Norman R., 2004. "A test for the distributional comparison of simulated and historical data," Economics Letters, Elsevier, vol. 85(2), pages 185-193, November.
  8. Valentina Corradi & Norman Swanson, 2003. "The Block Bootstrap for Parameter Estimation Error In Recursive Estimation Schemes, With Applications to Predictive Evaluation," Departmental Working Papers 200313, Rutgers University, Department of Economics.
  9. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics.
  10. Stefania D'Amico, 2005. "Density selection and combination under model ambiguity: an application to stock returns," Finance and Economics Discussion Series 2005-09, Board of Governors of the Federal Reserve System (U.S.).

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