  Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with
unknown distribution. Our goal is to estimate the conditional expectation of
$X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly
consistent way. Bailey and Ryabko proved that this is not possible even for
ergodic binary time series if one estimates at all values of $n$. We propose a
very simple algorithm which will make prediction infinitely often at carefully
selected stopping times chosen by our rule. We show that under certain
conditions our procedure is strongly (pointwise) consistent, and $L_2$
consistent without any condition. An upper bound on the growth of the stopping
times is also presented in this paper.
