Biological Cybernetics

, Volume 66, Issue 2, pp 159–165 | Cite as

Non-linear and linear forecasting of the EEG time series

  • K. J. Blinowska
  • M. Malinowski


The method of non-linear forecasting of time series was applied to different simulated signals and EEG in order to check its ability of distinguishing chaotic from noisy time series. The goodness of prediction was estimated, in terms of the correlation coefficient between forecasted and real time series, for non-linear and autoregressive (AR) methods. For the EEG signal both methods gave similar results. It seems that the EEG signal, in spite of its chaotic character, is well described by the AR model.


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  1. Babloyantz A, Destexte A (1987) Strange attractors in the human cortex. Springer Series in Synergetics, vol 36, Springer, Berlin Heidelberg New York, pp 48–56Google Scholar
  2. Babloyantz A (1989) Estimation of correlation dimension from single and multichannel recordings — a critical review. Springer Series in Brain Dynamics, vol 2. Springer, Berlin Heidelberg New York, pp 122–130Google Scholar
  3. Bendat JS, Piersol AG (1986) Random data: analysis and measurement procedures, 2nd edn. Wiley New YorkGoogle Scholar
  4. Blinowska KJ, Franaszczuk PJ (1989) A model of the generation of electrocortical rhythms. Springer Series in Brain Dynamics, vol 2. Springer, Berlin Heidelberg New York, pp 192–201Google Scholar
  5. Blinowska KJ, Franaszczuk PJ, Mitraszewski P (1988) A new method of presentation of the average spectral properties of the EEG time series. Int J Biomed Comput 22:97–106Google Scholar
  6. Eckman JP, Oliffson Kamphorst S, Ruelle D (1987) Recurrence plots of dynamical systesm. Europhys Lett 4:973–977Google Scholar
  7. Farmer JD, Sidorovich JJ (1987) Predicting chaotic time series. Phys Rev Lett 59:845–848Google Scholar
  8. Franaszczuk PJ, Blinowska KJ, Kowalczyk M (1985) The application of parametric multichannel spectral estimates in the study of electric brain activity. Biol Cybern 51:239–247Google Scholar
  9. Franaszczuk PJ, Blinowska KJ (1985) Linear model of brain electrical activity, EEG as a superposition of damped oscillatory modes. Biol Cybern 53:19–25Google Scholar
  10. Freeman WJ (1990) On the problem of anomalous dispersion in chaoto-chaotic phase transitions in neural masses and its significance for the management of perceptual information in brains. Springer Series in Synergetics, vol 45. Springer, Berlin Heidelberg New York, pp. 126–142Google Scholar
  11. Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D9:183–208Google Scholar
  12. Gershenfeld N (1988) An experimentalist's introduction to the observation of dynamical systems. In: Hao Bai-Liu (ed) Directions in chaos, vol II. World Scientific, Singapore New Jersey Hong Kong pp 310–382Google Scholar
  13. Layne SP, Meyer-Kress G, Holzfuss J (1986) Problems associated with dimensional analysis of electroencephalogram data. Springer Series Synergetics, vol 32. Springer, Berlin Heidelberg New York, pp 246–256Google Scholar
  14. Lopes da Silva FH, Van Rotterdam A, Barts P, Van Hensden E, Burr (1976) Models of neuronal populations. The basics mechanisms of rhythmicity. In: Corner MA, Swaab D (eds) Progress in brain research, vol 45. Elsevier/North Holland Biomedical Press, Amsterdam, pp 281–308Google Scholar
  15. Röschke J, Başar E (1989) Correlation dimensions in various parts of cat and human brain in different states. In: Springer Series in Brain Dynamics, vol 2. Springer, Berlin Heidelberg New York pp 131–157Google Scholar
  16. Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the word. Behav Sci 10:161–195Google Scholar
  17. Sugihara G, May RM (1990) Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734–741.Google Scholar
  18. Wright JJ (1990) Reticular activation and the dynamics of neuronal networks. Biol Cybern 62:289–298Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • K. J. Blinowska
    • 1
  • M. Malinowski
    • 1
  1. 1.Laboratory of Medical Physics, Warsaw UniversityWarszawaPoland

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