Kalman recursions Aggregated Online

Abstract

In this article, we aim to improve the prediction from experts’ aggregation by using the underlying properties of the models that provide the experts involved in the aggregation procedure. We restrict ourselves to the case where experts perform their predictions by fitting state-space models to the data using Kalman recursions. Using exponential weights, we construct different Kalman recursions Aggregated Online (KAO) algorithms that compete with the best expert or the best convex combination of experts in a more or less adaptive way. When the experts are Kalman recursions, we improve the existing results on experts’ aggregation literature, taking advantage of the second-order properties of the Kalman recursions. We apply our approach to Kalman recursions and extend it to the general adversarial expert setting by state-space modeling the experts’ errors. We apply these new algorithms to a real-data set of electricity consumption and show how they can improve forecast performances compared to other exponentially weighted average procedures.