Comparing Density Forecasts via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods
This paper proposes and analyzes tests that can be used to compare the accuracy of alternative conditional density forecasts of a variable. The tests are also valid in the broader context of model selection based on out-of-sample predictive ability. We restrict attention to the case of density forecasts derived from non-nested parametric models, with known or estimated parameters. The evaluation makes use of scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. In particular, we consider the logarithmic scoring rule, which leads to the development of asymptotic and bootstrap 'weighted likelihood ratio' tests. The name comes from the fact that the tests compare weighted averages of the scores over the available sample, as a way to focus attention on different regions of the distribution of the variable. For a uniform weight function, the asymptotic test can be interpreted as an extension of Vuong (1989)' s likelihood ratio test for non-nested hypotheses to time series data and to an out-of-sample testing framework. A Monte Carlo simulation explores the size and power properties of this last test in finite samples. An application using S&P500 daily returns shows how the tests can be used to compare the performance of density forecasts obtained from GARCH models with different distributional assumptions.
|Date of creation:||01 Jun 2002|
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- Peter F. Christoffersen & Francis X. Diebold, 1994.
"Optimal Prediction Under Asymmetric Loss,"
NBER Technical Working Papers
0167, National Bureau of Economic Research, Inc.
- 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.
- Peter F. Christoffersen & Francis X. Diebold, 1997. "Optimal prediction under asymmetric loss," Working Papers 97-11, Federal Reserve Bank of Philadelphia.
- Christoffersen & Diebold, . "Optimal Prediction Under Asymmetric Loss," Home Pages 167, 1996., University of Pennsylvania.
- Newey, Whitney K & West, Kenneth D, 1987.
"A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,"
Econometric Society, vol. 55(3), pages 703-08, May.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- 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.
- Francis X. Diebold & Jose A. Lopez, 1995.
"Forecast evaluation and combination,"
9525, Federal Reserve Bank of New York.
- West, Kenneth D, 1996.
"Asymptotic Inference about Predictive Ability,"
Econometric Society, vol. 64(5), pages 1067-84, September.
- Jose A. Lopez, 1995.
"Evaluating the predictive accuracy of volatility models,"
9524, Federal Reserve Bank of New York.
- 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.
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