A note on prediction for discrete time series

G. Morvai, Benjamin Weiss

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let {X n} be a stationary and ergodic time series taking values from a finite or countably infinite set X and that f(X) is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times λ n along which we will be able to estimate the conditional expectation E(f(X λn+1)|X 0, . . . ,X λn) from the observations (X 0, . . . ,X λn) in a point wise 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 (in particular, all stationary and ergodic Markov chains are included in this class) then limn→ ∞n/λ n > 0 almost surely. If the stationary and ergodic process turns out to possess finite entropy rate then λ n is upper bounded by a polynomial, eventually almost surely.

Original languageEnglish
Pages (from-to)809-823
Number of pages15
JournalKybernetika
Volume48
Issue number4
Publication statusPublished - 2012

Fingerprint

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

Keywords

  • Nonparametric estimation
  • Stationary processes

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Information Systems
  • Theoretical Computer Science
  • Electrical and Electronic Engineering

Cite this

A note on prediction for discrete time series. / Morvai, G.; Weiss, Benjamin.

In: Kybernetika, Vol. 48, No. 4, 2012, p. 809-823.

Research output: Contribution to journalArticle

Morvai, G & Weiss, B 2012, 'A note on prediction for discrete time series', Kybernetika, vol. 48, no. 4, pp. 809-823.
Morvai, G. ; Weiss, Benjamin. / A note on prediction for discrete time series. In: Kybernetika. 2012 ; Vol. 48, No. 4. pp. 809-823.
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