Guessing the output of a stationary binary time series - Mathematics > Probability

Abstract: 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.

Author: Gusztav Morvai

Source: https://arxiv.org/