Guessing the output of a stationary binary time series

TL;DR

This paper introduces a method for making infinitely often predictions of a stationary binary time series at carefully chosen stopping times, despite the impossibility of universal prediction at all times.

Contribution

The paper proposes a novel procedure for making infinitely often predictions at selected stopping times for stationary binary time series, with analysis of the stopping times' growth rate.

Findings

Predicts the next value at selected stopping times

Provides a growth rate analysis of stopping times

Demonstrates the feasibility of infinitely often prediction

Abstract

The forward prediction problem for a binary time series $\{X_n\}_{n=0}^{\infty}$ is to estimate the probability that $X_{n+1}=1$ 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. The growth rate of the stopping times is also exhibited.