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Modelling non-stationary variance in EEG time series by state space GARCH model

Kin Foon Kevin Wong, Andreas Galka, Okito Yamashita, Tohru Ozaki
2006 Computers in Biology and Medicine  
We present a new approach to modelling non-stationarity in EEG time series by a generalized state space approach.  ...  Non-stationarity is modelled by allowing the variances of the driving noises to change with time, depending on the state prediction error within the state space model.  ...  Acknowledgements The authors would like to thank Dr Roy John and Dr Leslie Prichep for providing the EEG data set and for dedicating their precious time to giving the authors comments and guidance.  ... 
doi:10.1016/j.compbiomed.2005.10.001 pmid:16293239 fatcat:ijlokxvurrddfoiixnfisvnrky

Decomposition of Neurological Multivariate Time Series by State Space Modelling

Andreas Galka, Kin Foon Kevin Wong, Tohru Ozaki, Hiltrud Muhle, Ulrich Stephani, Michael Siniatchkin
2010 Bulletin of Mathematical Biology  
State space modelling, a generalisation of classical ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data, while this information  ...  Three application examples are presented, one electrocardigram time series and two electroencephalogram (EEG) time series.  ...  Acknowledgments This work was supported by the by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) through project SFB 855 "Biomagnetic Sensing" and by the Japanese Society for the  ... 
doi:10.1007/s11538-010-9563-y pmid:20821065 fatcat:tkrsoqjdkbaqraqds3fcediqfm

StationPlot: A New Non-stationarity Quantification Tool for Detection of Epileptic Seizures [article]

Sawon Pratiher, Subhankar Chattoraj, Rajdeep Mukherjee
2018 arXiv   pre-print
In the Euclidean space, both trend-stationary (TS) & difference-stationary (DS) perturbations are comprehended by the asymmetric structure of StationPlot's region of interest (ROI).  ...  A novel non-stationarity visualization tool known as StationPlot is developed for deciphering the chaotic behavior of a dynamical time series.  ...  Andrzeja for making the EEG dataset publicly available.  ... 
arXiv:1811.04230v1 fatcat:3mxbisaizvfbpc46ttmuldjy6u

QMNET Talk: The need for interdisciplinary comparison when analyzing time series [article]

Ben Fulcher
Exponential smoothing GARCH models Hidden Markov models Gaussian Processes Piecewise splines State space models ARMA models Stationarity StatAv Sliding window measures Distribution  ...  infer dimensions of common variance across time-series features-informative low-dimensional representation of time-series datasets Swedish leaves Fulcher and Jones (2014) Flies in a tube Fulcher and  ... 
doi:10.6084/m9.figshare.12775748.v1 fatcat:3ozo64z3mvbutmi4eurj2uk3ea

Entropy Analysis of High-Definition Transcranial Electric Stimulation Effects on EEG Dynamics

Diego C. Nascimento, Gabriela Depetri, Luiz H. Stefano, Osvaldo Anacleto, Joao P. Leite, Dylan J. Edwards, Taiza E. G. Santos, Francisco Louzada Neto
2019 Brain Sciences  
This work discusses the use of entropy as a measurement of the complexity of time series, in the context of Neuroscience, due to the non-stationary characteristic of the data.  ...  Here we present an alternative statistical approach with sample analysis that provides a summary statistic accounting for the non-stationary nature of time series data.  ...  The Kullback-Leibler (KL) divergence is the most commonly presented in statistics, and the Approximate Entropy (ApEn) is described as useful in the case of non-stationary time series.  ... 
doi:10.3390/brainsci9080208 pmid:31434225 pmcid:PMC6721406 fatcat:ccht74gqkzhazjzonck4hxlfpm

Application of modern tests for stationarity to single-trial MEG data

Lech Kipiński, Reinhard König, Cezary Sielużycki, Wojciech Kordecki
2011 Biological cybernetics  
Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto-(MEG) or electroencephalography (EEG).  ...  One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided  ... 
doi:10.1007/s00422-011-0456-4 pmid:22095173 fatcat:edzcme6wkjh4bosaqbb3yxpnii

Multivariate Stochastic Volatility Modeling of Neural Data

Tung D Phan, Jessica A Wachter, Ethan A Solomon, Michael Kahana
2019 eLife  
Using medial temporal lobe (MTL) recordings from 96 neurosurgical patients, we show that time series models with volatility described by a multivariate stochastic latent-variable process and lagged interactions  ...  Using the directional connections between brain regions during complex cognitive process provided by the model, we uncovered perirhinal-hippocampal desynchronization in the MTL regions that is associated  ...  This work was supported by the DARPA Restoring Active Memory (RAM) program (Cooperative Agreement N66001-14-2-4032).  ... 
doi:10.7554/elife.42950 pmid:31368892 pmcid:PMC6697415 fatcat:iiwuhauhkfch7erpr647pmy5cm

Detecting the direction of causal time series

Jonas Peters, Dominik Janzing, Arthur Gretton, Bernhard Schölkopf
2009 Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09  
We propose a method that detects the true direction of time series, by fitting an autoregressive moving average model to the data.  ...  We test our approach on two types of data: simulated data sets conforming to our modeling assumptions, and real world EEG time series.  ...  the physical state space (Balian, 1992) ).  ... 
doi:10.1145/1553374.1553477 dblp:conf/icml/PetersJGS09 fatcat:tfgrdwebmvdspploenl66nlsqy

Random autoregressive models: A structured overview [article]

Marta Regis, Paulo Serra, Edwin R. van den Heuvel
2020 arXiv   pre-print
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series.  ...  Most models focus on one property of the data, while much can be gained by combining the strength of various models and their sources of heterogeneity.  ...  Conflict of interests No potential conflict of interest was reported by the authors.  ... 
arXiv:2009.08165v1 fatcat:ea5pt3vfxzg3je22imie2gpmbi

Surface myoelectric signal classification using the AR-GARCH model

Ghulam Rasool, Nidhal Bouaynaya, Kamran Iqbal, Gannon White
2014 Biomedical Signal Processing and Control  
We analyzed the myoelectric signal as a stochastic time-series and found that the signal is heteroscedastic, i.e., the AR modeling residuals exhibit a time-varying variance.  ...  Heteroscedasticity is a major concern in statistical modeling because it can invalidate statistical tests of significance which may assume that the modeling errors are uncorrelated and that the error variances  ...  The GARCH models have also been used within a state-space framework and the Kalman filter for modeling non-stationary variance in the EEG signal [16] , or modeling covariance for generation of the EEG  ... 
doi:10.1016/j.bspc.2014.06.001 fatcat:6lb3walqnjdsji6knqydx6bkba

Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise [article]

Niklas Pfister, Sebastian Weichwald, Peter Bühlmann, Bernhard Schölkopf
2019 arXiv   pre-print
Additionally, it can be used for applications with grouped data by adjusting for different stationary noise within each group.  ...  We show that our proposed general noise model allows to perform ICA in settings where other noisy ICA procedures fail.  ...  NP and PB were partially supported by the European Research Commission grant 786461 CausalStats -ERC-2017-ADG.  ... 
arXiv:1806.01094v3 fatcat:oq4j45o7kfftdluv634wwqn73i

CNS 2020 Tutorial: Characterizing neural dynamics using highly comparative time-series analysis [article]

Ben Fulcher
2020 Figshare  
Exponential smoothing GARCH models Hidden Markov models Gaussian Processes Piecewise splines State space models ARMA models Stationarity StatAv Sliding window measures Distribution  ...  series can be represented as algorithms that capture time-series properties as real numbers compute the optimal low-dimensional space in which to represent interesting differences in my dynamics, the  ... 
doi:10.6084/m9.figshare.12671900.v1 fatcat:laj2xvkkezckjd6bibmxhfnrqa

Algorithm for the Detection of Changes of the Correlation Structure in Multivariate Time Series

K. Pukenas
2012 Elektronika ir Elektrotechnika  
The set of D=10 uncoupled time series were generated by means of the Matlab GARCH module and applying data smoothing. The data were generated repeatedly in 20 independent trials.  ...  The form a new orthogonal basis in the embedding space of , and the corresponding give the variance in the direction of .  ... 
doi:10.5755/j01.eee.18.8.2625 fatcat:noepri77i5evfpv5hceyc7rjei

Time-series forecasting

Chris Chatfield
2005 Significance  
State-space models deal with non-stationary features like trend by including explicit terms for them in the model.  ...  Except in trivial cases, a state-space model will be non-stationary and hence will not have a time-invariant ac.f.  ...  CHAPTER 8 Model Uncertainty and Forecast Accuracy Much of the time-series literature implicitly assumes that there is a true model for a given time series and that this model is known before it is fitted  ... 
doi:10.1111/j.1740-9713.2005.00117.x fatcat:6vr4ec5vdfcqra3ecltvwod6mq

Measures of Analysis of Time Series (MATS): AMATLABToolkit for Computation of Multiple Measures on Time Series Data Bases

Dimitris Kugiumtzis, Alkiviadis Tsimpiris
2010 Journal of Statistical Software  
Measures related to specific toolboxes, such as GARCH models (McCullough and Renfro 1998), neural networks and wavelets, are not implemented in MATS.  ...  properties of the time series.  ...  on non-stationary time series.  ... 
doi:10.18637/jss.v033.i05 fatcat:astmfgxyebb3zlaqwj56biysgq
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