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Chi-squared tests of interval and density forecasts and the Bank of England's fan charts

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Author Info
Kenneth F. Wallis (University of Warwick - Department of Economics, Coventry CV4 7AL, United Kingdom.)

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Abstract

This paper reviews recently proposed likelihood ratio tests of goodness-of-fit and independence of interval forecasts. It recasts them in the framework of Pearson chi-squared statistics, and considers their extension to density forecasts and their exact small-sample distributions. The use of the familiar framework of contingency tables will increase the accessibility of these methods. The tests are applied to two series of density forecasts of inflation, namely the US Survey of Professional Forecasters and the Bank of England fan charts. This first evaluation of the fan chart forecasts finds that whereas the current-quarter forecasts are well-calibrated, this is less true of the one-year-ahead forecasts. The fan charts fan out too quickly, and the excessive concern with the upside risks was not justified over the period considered. JEL Classification: C53; E37.

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Paper provided by European Central Bank in its series Working Paper Series with number 083.

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Length: 32 pages
Date of creation: Nov 2001
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Handle: RePEc:ecb:ecbwps:20010083

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Related research
Keywords: Forecast evaluation; interval forecasts; density forecasts; likelihood ratio tests; chi-squared tests; exact inference; Bank of England inflation forecasts.;

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References listed on IDEAS
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. Thompson, Patrick A & Miller, Robert B, 1986. "Sampling the Future: A Bayesian Approach to Forecasting from Univariate Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 427-36, October.
  3. 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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  4. 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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  5. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  6. Michael P. Clements & Nick Taylor, 2003. "Evaluating interval forecasts of high-frequency financial data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 445-456. [Downloadable!]
  7. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January. [Downloadable!] (restricted)
  8. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society. [Downloadable!]
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Cited by:
(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. Christopher Spencer, 2006. "The Dissent Voting Behaviour of Bank of England MPC Members," Department of Economics Discussion Papers 0306, Department of Economics, University of Surrey. [Downloadable!]
  2. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F, 2004. "Sensitivity of the Chi-Squared Goodness-of-Fit Test to the Partitioning of Data," The Warwick Economics Research Paper Series (TWERPS) 694, University of Warwick, Department of Economics. [Downloadable!]
  3. B. Siliverstovs & D.J. Van Dijk, 2003. "Forecasting industrial production with linear, nonlinear and structural change models," Econometric Institute Report 321, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  4. Marco Vega, 2004. "Policy Makers Priors and Inflation Density Forecasts," Econometrics 0403005, EconWPA. [Downloadable!]
  5. Gianna Boero & Emanuela Marrocu, 2002. "The performance of Setar Models: a regime conditional evaluation of point, interval and density forecasts," Working Paper CRENoS 200208, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia. [Downloadable!]
    Other versions:
  6. Knüppel, Malte & Schultefrankenfeld, Guido, 2008. "How informative are macroeconomic risk forecasts? An examination of the Bank of England's inflation forecasts," Discussion Paper Series 1: Economic Studies 2008,14, Deutsche Bundesbank, Research Centre. [Downloadable!]
  7. Harris, Mark & Spencer, Christopher, 2008. "Decade of dissent: explaining the dissent voting behavior of Bank of England MPC members," MPRA Paper 9100, University Library of Munich, Germany. [Downloadable!]
  8. Gianna Boero & Emanuela Marrocu, 2001. "Evaluating non-linear models on point and interval forecasts: an application with exchange rate returns," Working Paper CRENoS 200110, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia. [Downloadable!]
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