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Causal coherence[40 42] or partial directed coherence[43, 44], based on multivariate autoregressive modeling may be used for this purpose.
Intracranial EEG recordings were analyzed with a multivariate autoregressive modeling technique (short-time direct directed transfer function SdDTF), based on the concept of Granger causality, to estimate the directionality and intensity of propagation of high frequency activity (70 175 Hz) during ictal and interictal recordings.
These relationships remained significant in multivariate autoregressive modeling.
GC uses multivariate autoregressive modeling to ascertain whether time series A may be more accurately predicted from time series B, with a certain time lag, than B from A. If incorporating values from B in the regression of A allows better prediction of A than vice versa, B is said to influence A. The data were first detrended and rendered zero mean across epochs to remove nonstationarity.
In cases of multiple time series, a first approach to infer connectivity would be to apply techniques such as multivariate autoregressive modeling (VAR), which allows identification of connectivity by combining graphical modeling methods with the concept of Granger causality [ 22].
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They also build multivariate autoregressive models for a smaller number of links.
Firstly, the Source Information Flow Toolbox (SIFT) [27] in the EEGLAB was used to identify the optimal multivariate autoregressive model.
A multivariate autoregressive model is presented, and its parameters are estimated by least squares via the implementation of QR factorization.
Granger causality has been increasingly used to identify causal influence between time series based on multivariate autoregressive models.
multiple window time frequency analysis (MW-TFA) [9], frequency-dependant correlation coefficient [10], time varying causal coherence function (TVCCF) based on the multivariate autoregressive model [11].
The VAR processes are a generalization of multivariate autoregressive models (AR), where each variable is regressed on a set of others with several lags (Hamilton 1994; Enders 2009).
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