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Prediction for discrete time series
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  • Published: 09 October 2004

Prediction for discrete time series

  • Gusztáv Morvai1 &
  • Benjamin Weiss2 

Probability Theory and Related Fields volume 132, pages 1–12 (2005)Cite this article

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  • 17 Citations

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Abstract.

Let {X n } be a stationary and ergodic time series taking values from a finite or countably infinite set 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(=x|X0,...,) from data segment (X0,...,) 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 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.

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References

  1. Bailey, D.H.: Sequential schemes for classifying and predicting ergodic processes. Ph.D. thesis, Stanford University, 1976

  2. Chung, K.L.: A note on the ergodic theorem of information theory. Ann. Math. Stat. 32, 612–614 (1961)

    MATH  Google Scholar 

  3. Cover, T.M., Thomas, J.: Elements of information theory. Wiley, 1991

  4. Csiszár, I., Shields, P.: The consistency of the BIC Markov order estimator. Ann. Stat. 28, 1601–1619 (2000)

    Article  Google Scholar 

  5. Csiszár, I.: Large-scale typicality of Markov sample paths and consistency of MDL order estimators. IEEE Trans. Inf. Theory 48, 1616–1628 (2002)

    Google Scholar 

  6. Devroye, L., Györfi, L., Lugosi, G.: A probabilistic theory of pattern recognition. Springer-Verlag, New York, 1996

  7. Györfi, L., Morvai, G., Yakowitz, S.: Limits to consistent on-line forecasting for ergodic time series. IEEE Trans. Inf. Theory 44, 886–892 (1998)

    Google Scholar 

  8. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Association 58, 13–30 (1963)

    MATH  Google Scholar 

  9. Kalikow, S.: Random Markov processes and uniform martingales. Israel J. Math. 71, 33–54 (1990)

    MATH  Google Scholar 

  10. Keane, M.: Strongly mixing g-measures. Invent. Math. 16, 309–324 (1972)

    MATH  Google Scholar 

  11. Morvai, G.: Guessing the output of a stationary binary time series. In: Foundations of Statistical Inference, Y. Haitovsky, H.R.Lerche, Y. Ritov (eds.), Physika-Verlag, 2003, pp. 207–215

  12. Morvai, G., Weiss, B.: Forecasting for stationary binary time series. Acta Applicandae Mathematicae 79, 25–34 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Révész, P.: The law of large numbers. Academic Press, 1968

  14. Ryabko, Ya.B.: Prediction of random sequences and universal coding. Problems of Inform. Trans. 24, 87–96 (1988)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Research Group for Informatics and Electronics of the Hungarian Academy of Sciences, Budapest, 1521, Goldmann György tér 3, Hungary

    Gusztáv Morvai

  2. Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Benjamin Weiss

Authors
  1. Gusztáv Morvai
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  2. Benjamin Weiss
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Corresponding author

Correspondence to Benjamin Weiss.

Additional information

Mathematics Subject Classification (2000): 62G05, 60G25, 60G10

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Morvai, G., Weiss, B. Prediction for discrete time series. Probab. Theory Relat. Fields 132, 1–12 (2005). https://doi.org/10.1007/s00440-004-0386-3

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  • Received: 06 September 2003

  • Revised: 30 June 2004

  • Published: 09 October 2004

  • Issue Date: May 2005

  • DOI: https://doi.org/10.1007/s00440-004-0386-3

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Keywords

  • Nonparametric estimation
  • Stationary processes
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