  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.
