On efficient point prediction systems
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 4
Abstract
Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every timet, issues a point prediction for the next observation at timet+1. We introduce the concept ofefficiencyof a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of squared prediction errors. Independence is not a requirement. Under weak conditions, the class of efficient point prediction systems is non-empty, and any two efficient point prediction systems will, in a certain strong sense, make asymptotically identical predictions for the infinite future. We discuss the efficiency of point prediction systems based on Bayesian predictive means, and on plugging in parameter estimates. The results are applied to probability forecasting and stochastic regression.
Keywords
Efficiency, Optimal predictors, Point prediction systems, Predictive inference, Prequential inference, Stochastic regression, Time series
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