ON sequential estimation and prediction for discrete time series

Gusztáv Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)417-437
Number of pages21
JournalStochastics and Dynamics
Issue number4
Publication statusPublished - Dec 1 2007


  • Nonparametric estimation
  • Stationary processes

ASJC Scopus subject areas

  • Modelling and Simulation

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