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

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  • Wallis, Kenneth F.

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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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 19 (2003)
Issue (Month): 2 ()
Pages: 165-175

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Handle: RePEc:eee:intfor:v:19:y:2003:i:2:p:165-175

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Web page: http://www.elsevier.com/locate/ijforecast

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  1. Lahiri, Kajal & Teigland, Christie, 1987. "On the normality of probability distributions of inflation and GNP forecasts," International Journal of Forecasting, Elsevier, vol. 3(2), pages 269-279.
  2. 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.
  3. 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.
  4. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  5. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
  6. Kenneth F. Wallis, 1999. "Asymmetric density forecasts of inflation and the Bank of England's fan chart," National Institute Economic Review, National Institute of Economic and Social Research, vol. 167(1), pages 106-112, January.
  7. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, . "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  8. 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.
  9. Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1998. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," Working Papers 98-15, New York University, Leonard N. Stern School of Business, Department of Economics.
  10. 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.
  11. Anderson, Gordon, 1994. "Simple tests of distributional form," Journal of Econometrics, Elsevier, vol. 62(2), pages 265-276, June.
  12. 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.
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