Consistent estimation of a general nonparametric regression function in time series

We propose an estimator of the conditional distribution of X t | X t − 1 , X t − 2 , … , and the corresponding regression function E ( X t | X t − 1 , X t − 2 , … ) , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.