Prediction for discrete time series

G. Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Let {X n } be a stationary and ergodic time series taking values from a finite or countably infinite set X. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λ n along which we will be able to estimate the conditional probability P(Xλ n+1=x|X 0,...,λ n) from data segment (X 0,...,λ n) in a pointwise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series which includes among others all stationary and ergodic finitarily Markovian processes. If the stationary and ergodic process turns out to be finitarily Markovian (among others, all stationary and ergodic Markov chains are included in this class) then lim n→∞ n/λ n > almost surely. If the stationary and ergodic process turns out to possess finite entropy rate then λ n is upperbounded by a polynomial, eventually almost surely.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalProbability Theory and Related Fields
Volume132
Issue number1
DOIs
Publication statusPublished - May 2005

Fingerprint

Ergodic Processes
Discrete-time
Series
Prediction
Stationary Process
Time series
Markovian Process
Stopping Time
Conditional probability
Markov chain
Entropy
Unknown
Polynomial
Estimate
Class

Keywords

  • Nonparametric estimation
  • Stationary processes

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Statistics and Probability

Cite this

Prediction for discrete time series. / Morvai, G.; Weiss, Benjamin.

In: Probability Theory and Related Fields, Vol. 132, No. 1, 05.2005, p. 1-12.

Research output: Contribution to journalArticle

Morvai, G. ; Weiss, Benjamin. / Prediction for discrete time series. In: Probability Theory and Related Fields. 2005 ; Vol. 132, No. 1. pp. 1-12.
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