### Abstract

Bailey showed that the general pointwise forecasting for stationary and ergodic time series has a negative solution. However, it is known that for Markov chains the problem can be solved. Morvai showed that there is a stopping time sequence {λ_{n}} such that P(X_{λn+1} = 1 X_{0},..., X_{λn}) can be estimated from samples (X_{0},..., X_{λn}) such that the difference between the conditional probability and the estimate vanishes along these stoppping times for all stationary and ergodic binary time series. We will show it is not possible to estimate the above conditional probability along a stopping time sequence for all stationary and ergodic binary time series in a pointwise sense such that if the time series turns out to be a Markov chain, the predictor will predict eventually for all n.

Original language | English |
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Pages (from-to) | 285-290 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 72 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 15 2005 |

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### Keywords

- Finite-order Markov chains
- Nonparametric estimation
- Prediction theory
- Stationary and ergodic processes

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Statistics and Probability Letters*,

*72*(4), 285-290. https://doi.org/10.1016/j.spl.2004.12.016