Interval Forecasts

In this chapter, we consider the evaluation of interval forecasts (also commonly referred to as prediction intervals). An interest in interval forecasts recognizes that the traditional emphasis on point estimates neglects any measure or assessment of the uncertainty surrounding the point forecast, or the ‘confidence’ that the forecaster has in the prediction. Point forecasts are sometimes provided with simple summary statistics about the forecaster’s historical track record, such as ex post root mean squared errors calculated for past forecasts, as a tacit admission that in most practical settings the likely range of outcomes will influence the usefulness of the forecast. Unfortunately the magnitude or variability of past forecast errors may offer little guidance to the uncertainties attached to current forecasts, if the conditional variance of the process is changing over time, as in the volatility models of Chapter 3.