Open Access
February 1996 Nonparametric inference for ergodic, stationary time series
Gusztáv Morvai, Sidney Yakowitz, László Györfi
Ann. Statist. 24(1): 370-379 (February 1996). DOI: 10.1214/aos/1033066215


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.


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Gusztáv Morvai. Sidney Yakowitz. László Györfi. "Nonparametric inference for ergodic, stationary time series." Ann. Statist. 24 (1) 370 - 379, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0855.62076
MathSciNet: MR1389896
Digital Object Identifier: 10.1214/aos/1033066215

Primary: 60G10 , 60G25 , 62G05

Keywords: Nonparametric regression , stationary ergodic process , universal prediction schemes

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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