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Kenneth F. Wallis

1 November 2001
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 Code
C53 : Mathematical and Quantitative Methods→Econometric Modeling→Forecasting and Prediction Methods, Simulation Methods
E37 : Macroeconomics and Monetary Economics→Prices, Business Fluctuations, and Cycles→Forecasting and Simulation: Models and Applications