Intermittent estimation of stationary time series

Details Intermittent estimation of stationary time series Intermittent estimation of stationary time series

2007-11-02

arxiv.org/abs/0711.0350v1

Test 13 (2004), no. 2, 525--542

Mathematics

Probability

Scientific paper

Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way. Bailey and Ryabko proved that this is not possible even for ergodic binary time series if one estimates at all values of $n$. We propose a very simple algorithm which will make prediction infinitely often at carefully selected stopping times chosen by our rule. We show that under certain conditions our procedure is strongly (pointwise) consistent, and $L_2$ consistent without any condition. An upper bound on the growth of the stopping times is also presented in this paper.

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