Nonparametric inference for ergodic, stationary time series

Research output: Contribution to journalArticle

42 Citations (Scopus)


The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability of the next observation, given the infinite past. Ornstein gave such a construction for the case that the values are from a finite set, and recently Algoet extended the scheme to time series with coordinates in a Polish space. The present study relates a different solution to the challenge. The algorithm is simple and its verification is fairly transparent. Some extensions to regression, pattern recognition and on-line forecasting are mentioned.

Original languageEnglish
Pages (from-to)370-379
Number of pages10
JournalAnnals of Statistics
Issue number1
Publication statusPublished - Feb 1996


  • Nonparametric regression
  • Stationary ergodic process
  • Universal prediction schemes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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