On efficient probability forecasting systems

We study the asymptotic behaviour of probability forecasting systems, and discuss their usefulness as inferential tools for statistical problems such as model verification and selection. Our theoretical setting is the prequential, or predictive sequential, framework proposed by Dawid (1984). We study especially the notion of prequential efficiency of a forecasting system and present some new results. We focus on plug-in, or estimative, forecasting systems, where the forecast distribution is generated by replacing the unknown parameter with an estimate.