Introduction

By a forecast will be meant any statement about ‘the future’, where the future is relative to the analyst’s viewpoint. So as well as the common sense notion of a forecast of what will happen tomorrow, or next Saturday, the term will equally apply to the outcome of the 1997 General Election made now but based on what was known at the end of 1996, for example. Forecasts are often constructed ex post as a way of evaluating a particular forecasting model or forecasting device, presumably with the hope that the past forecast performance of the model will serve as a useful guide to how well it might forecast in the future. In any event, forecasting the past as the ‘relative future’ means that forecasts can be evaluated as they are made, without having to wait to see what actually happens tomorrow, or on the coming Saturday, and a large sample of forecasts can be generated (with associated outcomes available), which might allow a statistical analysis of the forecast performance of the model. My forecast of rain might turn out to be wrong, but that might just be bad luck. Suppose my forecasting model is that I forecast rain in the afternoon if at 11 a.m. in the morning the cows in a certain field are lying down. Given daily observations on afternoon rainfall and the morning stance of cows over the last year, one could devise a statistical test of whether my forecasting model was a good predictor of meteorological conditions.