Skip to main content
Explore URMC


URMC / Labs / Wismüller Lab / Software


Large-Scale Granger Causality Toolbox

This software was developed using MATLAB* 2014a and contains all the functions required to perform large-scale Granger causality (lsGC) Analysis [1,2]. This method can be used to extract directed influence flow between every pair of time-series in a system. It is an extension to multivariate Granger Causality analysis for very large systems, such as functional MRI data sets. The principle of Granger causality is based on the concept of cross-predictability where the improvement in prediction quality of a time-series in the presence of another time-series is evaluated and quantified, revealing influence direction between the two series.

The flow of influence between individual time-series is obtained using predictive models such as vector auto-regressive (VAR) modelling. For systems with very large number of time-series N as compared to number of time points T (N>>T), calculating a multivariate Granger causality index is not possible as the parameter estimation in multivariate predictive modelling scheme is limited by T resulting in an underdetermined problem. To counter this problem, we introduce a linear dimension reduction step prior to performing VAR. Predictions are performed in the low-dimensional space which are transformed back to the original space using the inverse of the transformation function. This permits us to compare the prediction with the true time-series in the original space, resulting in an lsGC index for each pair of time-series in the system.


[1] Wismüller, A., Nagarajan, M.B., Witte, H., Pester, B., and Leistritz, L.: Pair-wise clustering of large-scale Granger causality index matrices for revealing communities. Proc. of SPIE 90381R (doi: 10.1117/12.2044340) (2014)

[2] DSouza, A.M., Abidin, A.Z., Leistritz, L., and Wismüller, A.: Large-Scale Granger Causality Analysis on Resting-State fMRI. Accepted for publication, SPIE Medical Imaging 2016


This software is free for academic non-commercial usage. If you use it, please cite above references [1,2].


Copyright Wismüller Computational Radiology Laboratory, November 2015 University of Rochester,  Adora D’Souza (

*MATLAB is a registered trademark of Mathworks, Inc.