Guessing the output of a stationary binary time series

摘要

The forward prediction problem for a binary time series$\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ basedon the observations $X_i$, $0\le i\le n$ without prior knowledge of thedistribution of the process $\{X_n\}$. It is known that this is not possible ifone estimates at all values of $n$. We present a simple procedure which willattempt to make such a prediction infinitely often at carefully selectedstopping times chosen by the algorithm. The growth rate of the stopping timesis also exhibited.