On Sequential Estimation and Prediction for Discrete Time Series

Details On Sequential Estimation and Prediction for Discrete Time Series On Sequential Estimation and Prediction for Discrete Time Series

2008-03-30

arxiv.org/abs/0803.4332v1

Stochastics and Dynamics, Vol. 7, No. 4. pp. 417-437, 2007

Mathematics

Probability

Scientific paper

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through the work of D. Bailey that no universal estimator for $\textbf{P}(X_{n+1}|X_0,X_1,...X_n)$ can be found which converges to the true estimator almost surely. Despite this result, for restricted classes of processes, or for sequences of estimators along stopping times, universal estimators can be found. We present here a survey of some of the recent work that has been done along these lines.

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