Inferring the conditional mean

Consider a stationary real-valued time series ${Xn}{n=0}^{\infty}$ with a priori unknown distribution. The goal is to estimate the conditional expectation $E(X{n+1}|X0,..., Xn)$ based on the observations $(X0,..., X_n)$ in a pointwise consistent way. It is well known that this is not possible at all values of $n$. We will estimate it along stopping times.