English

Nonparametric inference for ergodic, stationary time series

Probability 2008-06-19 v1 Information Theory math.IT

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.

Keywords

Cite

@article{arxiv.0711.0367,
  title  = {Nonparametric inference for ergodic, stationary time series},
  author = {G. Morvai and S. Yakowitz and L. Gyorfi},
  journal= {arXiv preprint arXiv:0711.0367},
  year   = {2008}
}
R2 v1 2026-06-21T09:39:19.437Z