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Comparing Density Forecsts via Weighted Likelihood Ratio Tests

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Author Info
Gianni Amisano
Raffaella Giacomini

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Abstract

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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  2. 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. [Downloadable!] (restricted)
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  3. Raffaella Giacomini & Halbert White, 2004. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series 2003-09, Department of Economics, UC San Diego. [Downloadable!]
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  4. 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. [Downloadable!] (restricted)
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  5. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December. [Downloadable!]
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  9. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October. [Downloadable!] (restricted)
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  10. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
  11. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March. [Downloadable!] (restricted)
  12. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics. [Downloadable!]
  13. Clements, M.P. & Smith J., 1998. "Evaluating The Forecast of Densities of Linear and Non-Linear Models: Applications to Output Growth and Unemployment," The Warwick Economics Research Paper Series (TWERPS) 509, University of Warwick, Department of Economics.
  14. Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1997. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," NBER Working Papers 6228, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, 1997. "Evaluating Density Forecasts," NBER Technical Working Papers 0215, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  16. 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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  17. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05. [Downloadable!] (restricted)
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  18. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
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  19. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society. [Downloadable!]
  20. Weiss, Andrew A, 1996. "Estimating Time Series Models Using the Relevant Cost Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 539-60, Sept.-Oct. [Downloadable!] (restricted)
  21. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2008. "Partial Likelihood-Based Scoring Rules for Evaluating Density Forecasts in Tails," Discussion Papers 2008-10, School of Economics, The University of New South Wales. [Downloadable!]
    Other versions:
  2. Daniel Buncic, 2009. "Understanding forecast failure of ESTAR models of real exchange rates," EERI Research Paper Series EERI_RP_2009_18, Economics and Econometrics Research Institute (EERI). [Downloadable!]
  3. John M Maheu & Thomas H McCurdy, 2008. "Do high-frequency measures of volatility improve forecasts of return distributions?," Working Papers tecipa-324, University of Toronto, Department of Economics. [Downloadable!]
    Other versions:
  4. Diks, C.G.H. & Dijk, D. van & Panchenko, V., 2008. "Out-of-sample comparison of copula specifications in multivariate density forecasts," CeNDEF Working Papers 08-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
    Other versions:
  5. Manzan, Sebastiano & Zerom, Dawit, 2009. "Are Macroeconomic Variables Useful for Forecasting the Distribution of U.S. Inflation?," MPRA Paper 14387, University Library of Munich, Germany. [Downloadable!]
  6. Buncic, Daniel, 2009. "Understanding forecast failure of ESTAR models of real exchange rates," MPRA Paper 16525, University Library of Munich, Germany. [Downloadable!]
  7. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics. [Downloadable!]
  8. Ali Dib & Mohamed Gammoudi & Kevin Moran, 2006. "Forecasting Canadian Time Series With the New-Keynesian Model," Working Papers Central Bank of Chile 382, Central Bank of Chile. [Downloadable!]
    Other versions:
  9. Buncic, Daniel, 2009. "Understanding forecast failure in ESTAR models of real exchange rates," MPRA Paper 13121, University Library of Munich, Germany. [Downloadable!]
  10. John Geweke & Gianni Amisano, 2008. "Comparing and evaluating Bayesian predictive distributions of asset returns," Working Paper Series 969, European Central Bank. [Downloadable!]
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