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Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051919. Epub 2012 Nov 29.

Tracking time-varying causality and directionality of information flow using an error reduction ratio test with applications to electroencephalography data.

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Department of Automatic Control and System Engineering, University of Sheffield, Sheffield, United Kingdom.


This paper introduces an error reduction ratio-causality (ERR-causality) test that can be used to detect and track causal relationships between two signals. In comparison to the traditional Granger method, one significant advantage of the new ERR-causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Numerical examples are provided to illustrate the effectiveness of the new method together with the determination of the causality between electroencephalograph signals from different cortical sites for patients during an epileptic seizure.

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