Forecasting for stationary binary time series

Details Forecasting for stationary binary time series Forecasting for stationary binary time series

2007-10-26

arxiv.org/abs/0710.5144v1

Acta Appl. Math. 79 (2003), no. 1-2, 25--34

Mathematics

Probability

Scientific paper

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.

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