A consistent deterministic regression tree for non-parametric prediction of time series

TL;DR

This paper introduces a deterministic regression tree for online prediction of bounded stationary ergodic processes, achieving asymptotic optimality and matching the performance of the best Lipschitz predictors.

Contribution

It presents a novel deterministic regression tree method for non-parametric time series prediction with proven asymptotic optimality.

Findings

Achieves asymptotic regret bounds comparable to the best Lipschitz predictors.

Proves optimality within the class of bounded stationary ergodic processes.

Provides a new approach for online non-parametric time series prediction.

Abstract

We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best L-Lipschitz constant predictors. Then, we show why the obtained regret bound entails the asymptotical optimality with respect to the class of bounded stationary ergodic processes.