Modeling of time series using random forests: theoretical developments
This provides theoretical foundations for applying random forests to time series, which is incremental as it extends existing methods to a new setting.
The paper tackles the lack of theoretical justification for using random forests in nonlinear time series modeling by proving a uniform concentration inequality for regression trees and consistency for a class of random forests under mild conditions, supported by simulations.
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.