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New causality with adaptive model order and its applications to motor imagery EEG

Granger causality (GC) has been widely applied into the investigation of the directed functional connectivity from neurophysiological data, and however conventional GC approaches is based on the vector autoregressive (VAR) model in which the delay-dependent structure and the influence of model coefficients on causal relevance are not taken into account. In this paper, a novel causality analysis method is proposed based on modified causality measure and adaptive estimation of the orders of lagged variables. Firstly, the modified backward-in-time-selection (mBTS) algorithm is used for multivariate time series to dynamically select the lag order of each variable in basic VAR model. Secondly, a restricted VAR model is established using the appropriate set of orders and explanatory vectors found by mBTS. Then, the residuals and coefficients of the model are used to redefine the strength of cause-effect relationship between the variables. Compared with traditional GC, conditional GC (CGC), new causality (NC), new conditional causality (NCC), conditional GC based on time-ordered restricted VAR model (CGCI), the experimental results of simulations and real motor imagery EEG data verify the effectiveness of the proposed method.