Modeling of time series using random forests: theoretical developments

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.