Nonparametric inference for ergodic, stationary time series

Nonparametric inference for ergodic, stationary time series

Gusztáv Morvai, Sidney Yakowitz, and László Györfi

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

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.

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Primary Subjects: 60G10, 60G25, 62G05

Keywords: Universal prediction schemes; stationary ergodic process; nonparametric regression

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1033066215
Mathematical Reviews number (MathSciNet): MR1389896
Digital Object Identifier: doi:10.1214/aos/1033066215
Zentralblatt MATH identifier: 0855.62076

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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

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