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Comparing Density Forecsts via Weighted Likelihood Ratio Tests

  • Gianni Amisano
  • Raffaella Giacomini

We propose a test for comparing the out-of-sample accuracy of competing density forecasts of a variable. The test is valid under general conditions: the data can be heterogeneous and the forecasts can be based on (nested or non-nested) parametric models or produced by semi- parametric, non-parametric or Bayesian estimation techniques. The evaluation is based on scoring rules, which are loss functions de?ned over the density forecast and the realizations of the variable. We restrict attention to the logarithmic scoring rule and propose an out-of-sample weighted likelihood ratio test that compares weighted averages of the scores for the competing forecasts. The user-defined weights are a way to focus attention on di¤erent regions of the distribution of the variable. For a uniform weight function, the test can be interpreted as an extension of Vuong (1989)'s likelihood ratio test to time series data and to an out-of-sample testing framework. We apply the tests to evaluate density forecasts of US inflation produced by linear and Markov Switching Phillips curve models estimated by either maximum likelihood or Bayesian methods. We conclude that a Markov Switching Phillips curve estimated by maximum likelihood produces the best density forecasts of inflation.

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Paper provided by University of Brescia, Department of Economics in its series Working Papers with number ubs0504.

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Date of creation: 2005
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Handle: RePEc:ubs:wpaper:ubs0504
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  3. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, June.
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  7. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics.
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  19. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
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