Granger Causality in Multi-variate Time Series using a Time Ordered Restricted Vector Autoregressive Model

摘要

Granger causality has been used for the investigation of the inter-dependencestructure of the underlying systems of multi-variate time series. Inparticular, the direct causal effects are commonly estimated by the conditionalGranger causality index (CGCI). In the presence of many observed variables andrelatively short time series, CGCI may fail because it is based on vectorautoregressive models (VAR) involving a large number of coefficients to beestimated. In this work, the VAR is restricted by a scheme that modifies therecently developed method of backward-in-time selection (BTS) of the laggedvariables and the CGCI is combined with BTS. Further, the proposed approach iscompared favorably to other restricted VAR representations, such as thetop-down strategy, the bottom-up strategy, and the least absolute shrinkage andselection operator (LASSO), in terms of sensitivity and specificity of CGCI.This is shown by using simulations of linear and nonlinear, low andhigh-dimensional systems and different time series lengths. For nonlinearsystems, CGCI from the restricted VAR representations are compared withanalogous nonlinear causality indices. Further, CGCI in conjunction with BTSand other restricted VAR representations is applied to multi-channel scalpelectroencephalogram (EEG) recordings of epileptic patients containingepileptiform discharges. CGCI on the restricted VAR, and BTS in particular,could track the changes in brain connectivity before, during and afterepileptiform discharges, which was not possible using the full VARrepresentation.