The Annals of Statistics

Nonparametric inference for ergodic, stationary time series

Gusztáv Morvai, Sidney Yakowitz, and László Györfi

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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.

Article information

Source
Ann. Statist., Volume 24, Number 1 (1996), 370-379.

Dates
First available in Project Euclid: 26 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1033066215

Digital Object Identifier
doi:10.1214/aos/1033066215

Mathematical Reviews number (MathSciNet)
MR1389896

Zentralblatt MATH identifier
0855.62076

Subjects
Primary: 60G10: Stationary processes 60G25: Prediction theory [See also 62M20] 62G05: Estimation

Keywords
Universal prediction schemes stationary ergodic process nonparametric regression

Citation

Morvai, Gusztáv; Yakowitz, Sidney; Györfi, László. Nonparametric inference for ergodic, stationary time series. Ann. Statist. 24 (1996), no. 1, 370--379. doi:10.1214/aos/1033066215. https://projecteuclid.org/euclid.aos/1033066215


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  • TUCSON, ARIZONA 85721 1521 STOCZEK U. 2, BUDAPEST HUNGARY LASZLO Gy ORFI ´ ´ ¨ DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE TECHNICAL UNIVERSITY OF BUDAPEST 1521 STOCZEK U. 2, BUDAPEST HUNGARY