Multivariate time series analysis of neuroscience data: some challenges and opportunities

•Inverting estimated high dimensional spectral density matrix has computational problems.•Invoking sparsity principal, direct estimates of precision matrix has led to interpretable Gaussian graphs.•Graphical modeling of multivariate time series is essential in studying effective connectivity.•Granger non-causality decision depends on the available model covariates.•The dimensionality reduction for the confounding and response processes should be treated differently.

Neuroimaging data may be viewed as high-dimensional multivariate time series, and analyzed using techniques from regression analysis, time series analysis and spatiotemporal analysis. We discuss issues related to data quality, model specification, estimation, interpretation, dimensionality and causality. Some recent research areas addressing aspects of some recurring challenges are introduced.