Prequential probability: principles and properties
Forcaster has to predict, sequentially, a string of uncertain quantities (X1, X2, .. .), whose values are determined and revealed, one by one, by Nature. Various criteria may be proposed to assess Forecaster's empirical performance. The weak prequential principle requires that such a criterion should depend on Forecaster's behaviour or strategy only through the actual forecasts issued. A wide variety of appealing criteria are shown to respect this principle. We further show that many such criteria also obey the strong prequential principle, which requires that, when both Nature and