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Granger causality for sets of time series in the frequency domain, with applications in neuroscience

Grant number: 12/12320-7
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): August 01, 2012
Effective date (End): September 30, 2014
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
Principal Investigator:André Fujita
Grantee:Gustavo Pinto Vilela
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The study of time series is important in identifying the direction of the information flow between two random variables, since it allows verifying the influence of past values on a given instant value. Based on the intuitive concept that an effect never precedes its cause, Wiener (1956) and Granger (1969) introduced the idea that if the information of past values of a time series statistically improves the prediction of a second series, then there is a "causal" relationship (Granger causality) from the first one to the second. The idea was generalized, first by Geweke (1984) to identify Granger causality from a set of series to another series and later, by Fujita et al. (2010), to identify Granger causality for sets of time series. The latter model has the limitation that the analysis is only possible in the temporal domain. The identification of the frequency of the information flow is only possible in a frequency domain analysis, which in Neuroscience would allow filtering from the data, possible non-neurological signals that interfere in the results comprehension and in understanding how several brain areas communicate with each other. The PDC (Partial Directed Coherence) technique is used to identify Granger causality in the frequency domain but its generalization for sets of time series is unknown. Therefore, this project aims to overcome this limitation proposing a model to identify Granger causality for sets of time series in the frequency domain. The developed technique will be applied on actual functional Magnetic Resonance Imaging (fMRI) and/or Electroencephalography (EEG) data and thus, it is expected to improve the understanding of the functional network of the brain and consequently the complex human behavior. (AU)