Nonparametric inference for ergodic, stationary time series

G. Morvai; S. Yakowitz; L. Gyorfi

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arXiv · 0711.0367

Nonparametric inference for ergodic, stationary time series

G. Morvai·S. Yakowitz·L. Gyorfi

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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.

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BibTeX RIS

G. Morvai, S. Yakowitz, L. Gyorfi. 2007-11-02. Nonparametric inference for ergodic, stationary time series. https://arxiv.org/abs/0711.0367

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