  The forecasting problem for a stationary and ergodic binary time series
$\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ based
on the observations $X_i$, $0\le i\le n$ without prior knowledge of the
distribution of the process $\{X_n\}$. It is known that this is not possible if
one estimates at all values of $n$. We present a simple procedure which will
attempt to make such a prediction infinitely often at carefully selected
stopping times chosen by the algorithm. We show that the proposed procedure is
consistent under certain conditions, and we estimate the growth rate of the
stopping times.
