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On Sequential Estimation and Prediction for Discrete Time Series

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  • Gusztav Morvav
  • Benjamin Weiss

Abstract

The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process X0,X1,…,Xn 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 P(Xn+1|X0,X1, ...Xn) 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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  • Gusztav Morvav & Benjamin Weiss, 2007. "On Sequential Estimation and Prediction for Discrete Time Series," Discussion Paper Series dp464, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp464
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    1. Gusztáv Morvai & Benjamin Weiss, 2004. "Intermittent estimation of stationary time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 525-542, December.
    2. Morvai, Gusztáv & Weiss, Benjamin, 2005. "Limitations on intermittent forecasting," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 285-290, May.
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