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}
}