Modeling of time series using random forests: theoretical developments

TL;DR

This paper establishes the theoretical foundations for using random forests in nonlinear time series modeling, proving consistency and concentration inequalities under mild conditions, supported by simulations.

Contribution

It provides the first theoretical analysis of random forests applied to nonlinear time series, including consistency proofs and concentration inequalities.

Findings

Proves a uniform concentration inequality for regression trees on nonlinear autoregressive processes.

Establishes consistency of random forests in the time series context.

Supports theoretical results with simulation studies.

Abstract

In this paper we study asymptotic properties of random forests within the framework of nonlinear time series modeling. While random forests have been successfully applied in various fields, the theoretical justification has not been considered for their use in a time series setting. Under mild conditions, we prove a uniform concentration inequality for regression trees built on nonlinear autoregressive processes and, subsequently, we use this result to prove consistency for a large class of random forests. The results are supported by various simulations.