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Nonparametric inference for ergodic, stationary time series

Authors
  • Morvai, G.
  • Yakowitz, S.
  • Gyorfi, L.
Type
Published Article
Publication Date
Nov 02, 2007
Submission Date
Nov 02, 2007
Identifiers
arXiv ID: 0711.0367
Source
arXiv
License
Unknown
External links

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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