Forward estimation for ergodic time series

Gusztáv Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

12 Citations (Scopus)


The forward estimation problem for stationary and ergodic time series {Xn}n=0 taking values from a finite alphabet X is to estimate the probability that Xn+1 = x based on the observations Xi, 0 ≤ i ≤ n without prior knowledge of the distribution of the process {Xn}. We present a simple procedure gn which is evaluated on the data segment (X0,...,Xn) and for which, error (n) = gn(x) - P (Xn+1= x X0,..., Xn) → 0 almost surely for a subclass of all stationary and ergodic time series, while for the full class the Cesaro average of the error tends to zero almost surely and moreover, the error tends to zero in probability.

Original languageEnglish
Pages (from-to)859-870
Number of pages12
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number5
Publication statusPublished - Sep 1 2005


  • Nonparametric estimation
  • Stationary processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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