Nonparametric inference for ergodic, stationary time series

G. Morvai, Sidney Yakowitz, L. Györfi

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

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
Volume24
Issue number1
Publication statusPublished - Feb 1996

Fingerprint

Nonparametric Inference
Stationary Time Series
Time series
Polish Space
Consistent Estimator
Conditional probability
Pattern Recognition
Forecasting
Finite Set
Regression
Stationary time series
Inference
Observation
Pattern recognition
Estimator

Keywords

  • Nonparametric regression
  • Stationary ergodic process
  • Universal prediction schemes

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Nonparametric inference for ergodic, stationary time series. / Morvai, G.; Yakowitz, Sidney; Györfi, L.

In: Annals of Statistics, Vol. 24, No. 1, 02.1996, p. 370-379.

Research output: Contribution to journalArticle

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