Consistent estimation of a general nonparametric regression function in time series

Abstract

We propose an estimator of the conditional distribution of Xt|Xt−1,Xt−2,…, and the corresponding regression function E(Xt|Xt−1,Xt−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.