Generalized state-space models for modeling nonstationary EEG time-series

Chapter
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 4)

Abstract

In this chapter we discuss a comprehensive framework for decomposing nonstationary time-series into a set of constituent processes. Our methodology is based on autoregressive moving-average (ARMA) modeling and on state-space modeling. For the purpose of modeling nonstationary phenomena, such as sudden phase transitions in dynamical behavior, we employ “generalized autoregressive conditional heteroscedastic modeling” (GARCH modeling), a technique originally introduced in the field of financial data analysis; however, this technique first needs to be generalized to the case of state-space modeling. Models are obtained through maximum-likelihood estimation; the innovation approach to time-series prediction helps us to derive an approximative expression for the likelihood of given data. We present three application examples relevant to the analysis of nonstationary phenomena in EEG time-series; the first case is the transition from the conscious state into anesthesia in a human patient, the second is the transition into epileptic seizure in a human patient, and the third is the transition between two sleep stages in a sheep fetus. The modeling algorithm does not require any prior information on the timing of such nonstationary phenomena.

Keywords

time-series analysis ARMA model state-space model Kalman filtering innovation approach nonstationarity GARCH model 

Notes

Acknowledgement

The work of A. Galka was supported by Deutsche Forschungsgemeinschaft (DFG) through SFB 654 “Plasticity and Sleep”. The anesthesia EEG data set was kindly provided by W.J. Kox and S. Wolter, Department of Anesthesiology and Intensive Care Medicine, Charité-University Medicine, Berlin, Germany, and by E.R. John, Brain Research Laboratories, New York University School of Medicine, New York, USA. The fetal sleep data set was kindly provided by A. Steyn-Ross, Department of Engineering, University of Waikato, New Zealand. The epilepsy EEG data set was kindly provided by K. Lehnertz and C. Elger, Clinic for Epileptology, University of Bonn, Germany.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of NeurologyUniversity of KielKielGermany
  2. 2.Massachusetts General HospitalHarvard Medical SchoolBostonUSA
  3. 3.Tohoku UniversityAoba-kuJapan

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