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

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 extends them to density forecasts. Two further recent developments are also incorporated, namely a more informative decomposition of the goodness-of-fit statistic, and the calculation of exact P-values. Examples considered are the US Survey of Professional Forecasters density forecasts of inflation and the Bank of England fan charts. This first evaluation of the Bank forecasts finds that the fan charts fan out too quickly, and the excessive concern with the upside risks was not justified.

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

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, E37interval and density forecasts

Density Forecasting: A Survey

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts.

THE PROPERTIES OF SOME GOODNESS-OF-FIT TESTS

The properties of Pearson’s goodness-of-fit test, as used in density forecast evaluation, income distribution analysis and elsewhere, are analysed. The components-of-chi-squared or “Pearson analog” tests of Anderson (1994) are shown to be less generally applicable than was originally claimed. For the case of equiprobable classes, where the general components tests remain valid, a Monte Carlo study shows that tests directed towards skewness and kurtosis may have low power, due to differences between the class boundaries and the intersection points of the distributions being compared. The power of individual component tests can be increased by the use of nonequiprobable classes.Pearson’s Goodness-of-fit test ; Component tests ; Distributional assumptions ; Monte Carlo ; Normality ; Nonequiprobable partitions

Uncertainty and disagreement in economic prediction : the Bank of England Survey of External Forecasters

This article introduces a new source of survey data, namely the Bank of England Survey of External Forecasters. The survey collects point and density forecasts of inflation and GDP growth, and hence offers the opportunity of constructing direct measures of uncertainty. We present a simple statistical framework in which to define and interrelate measures of uncertainty and disagreement. The resulting measures are compared with other direct measures of uncertainty, nationally and internationally. A significant, sustained reduction in inflation uncertainty followed the 1997 granting of operational independence to the Bank of England to pursue a monetary policy of inflation targeting.Forecast surveys ; point forecasts ; density forecasts ; uncertainty ; disagreement