### 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.

Original language | English |
---|---|

Pages (from-to) | 370-379 |

Number of pages | 10 |

Journal | Annals of Statistics |

Volume | 24 |

Issue number | 1 |

Publication status | Published - Feb 1996 |

### Fingerprint

### Keywords

- Nonparametric regression
- Stationary ergodic process
- Universal prediction schemes

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Statistics*,

*24*(1), 370-379.

**Nonparametric inference for ergodic, stationary time series.** / Morvai, G.; Yakowitz, Sidney; Györfi, L.

Research output: Contribution to journal › Article

*Annals of Statistics*, vol. 24, no. 1, pp. 370-379.

}

TY - JOUR

T1 - Nonparametric inference for ergodic, stationary time series

AU - Morvai, G.

AU - Yakowitz, Sidney

AU - Györfi, L.

PY - 1996/2

Y1 - 1996/2

N2 - 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.

AB - 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.

KW - Nonparametric regression

KW - Stationary ergodic process

KW - Universal prediction schemes

UR - http://www.scopus.com/inward/record.url?scp=0030551977&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030551977&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030551977

VL - 24

SP - 370

EP - 379

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 1

ER -