Spatio-temporal correlations from fMRI time series based on the NN-ARx model

For the purpose of statistical characterization of the spatio-temporal correlation structure of brain functioning from high-dimensional fMRI time series we introduce an innovation approach. This is based on whitening the data by the Nearest-Neighbors AutoRegressive model with eXternal inputs (NN-ARx). Correlations between the resulting innovations are an extension of the usual correlations, in which meancorrection is carried out by the dynamic NN-ARx model instead of the static, standard linear model for fMRI time series. Measures of dependencies between regions are defined by summarizing correlations among innovations at several time lags over pairs of voxels. Such summarization does not involve averaging the data over each region, which prevents loss of information in case of non-homogeneous regions. Statistical tests based on these measures are elaborated, which allow for assessing the correlation structure in search of connectivity. Results of application of the NNARx approach to fMRI data recorded in visual stimuli experiments are shown. Finally,