Kalman Recursions Aggregated Online

TL;DR

This paper introduces Kalman Recursions Aggregated Online (KAO), a novel method that leverages the properties of Kalman filters for expert prediction aggregation, improving forecast accuracy in real-world electricity consumption data.

Contribution

It develops new algorithms that utilize second-order properties of Kalman recursions for adaptive expert aggregation, extending to adversarial settings with state-space modeling.

Findings

Improved forecast accuracy over existing methods.

Effective in real electricity consumption data.

Extends to adversarial expert settings.

Abstract

In this article, we aim at improving the prediction of expert aggregation by using the underlying properties of the models that provide expert predictions. We restrict ourselves to the case where expert predictions come from Kalman recursions, fitting state-space models. By using exponential weights, we construct different algorithms of Kalman recursions Aggregated Online (KAO) that compete with the best expert or the best convex combination of experts in a more or less adaptive way. We improve the existing results on expert aggregation literature when the experts are Kalman recursions by 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 errors of the experts. We apply these new algorithms to a real dataset of electricity consumption and show how it can improve forecast performances comparing to other exponentially weighted average procedures.