Vector autoregressive (VAR) model is one of the most used models in the analysis of relationships inferences between time series, mainly because its parameters estimation is simple and the interpretation of statistical results is intuitive. In the analysis of fMRI data, Granger causality methods based on VAR models have been used to infer effective and functional connectivity between brain regions. However, stationarity condition is usually not valid in many real data applications. Furthermore, the BOLD signal measured in fMRI can be influenced by artifacts that may generate spurious correlation between the series. Finally, the high dimensionality of the data is an obstacle to infer relationships between neural modules. In order to deal with these problems, we introduce the Dynamic Vector Autoregressive Model based on Wavelets expansion, Partial Directed Coherence Analysis of fMRI data and the Cluster Granger Analysis. The foundations, asymptotic properties, computer intensive simulations and applications to real datasets are presented.

Keywords: Granger Causality; Neuroimaging; Connectivity; Time series

Biography: João Ricardo Sato has obtained his diploma, master and PhD title in Statistics at the Institute of Mathematics, Computation and Cognition, University of São Paulo, Brasil. Since 2009 he is a lecturer at the Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, Brazil. His main research is focused on multivariate time series analysis, econometrics, quantitative methods in Neuroscience and statistical processing of Neuroimaging data.