Chi-Squared Tests of Interval and Density Forecasts, and the Bank of England's Fan Charts

32 Pages Posted: 27 Feb 2003

See all articles by Kenneth F. Wallis

Kenneth F. Wallis

University of Warwick - Department of Economics

Date Written: November 2001

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.

Keywords: Forecast evaluation, interval forecasts, density forecasts, likelihood ratio tests, chi-squared tests, exact inference, Bank of England inflation forecasts

JEL Classification: C53, E37

Suggested Citation

Wallis, Kenneth F., Chi-Squared Tests of Interval and Density Forecasts, and the Bank of England's Fan Charts (November 2001). ECB Working Paper No. 83. Available at SSRN: https://ssrn.com/abstract=356260

Kenneth F. Wallis (Contact Author)

University of Warwick - Department of Economics ( email )

Coventry CV4 7AL
United Kingdom

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