Forecasting point and continuous processes: Prequential analysis

Summary The problem considered in this paper is that of evaluating the performance of a forecaster who predicts the intensity of a point process or the dirft and diffusion rates of a continuous process. It is shown that we can evaluate this performance in a “prequential” manner, without the usual assumption that the forecasts are generated in accordance with some probability distribution. Technically, the results in this paper are prequential counterparts of the Dambis-Dubins-Schwarz reduction of a continuous martingale, via a change of time, to a Wiener process, and the Papangelou-Meyer reduction of a counting process to a Poisson process.