Blockwise Granger causality and blockwise new causality

Multivariate blockwise Granger causality (BGC) is used to reflect causal interactions among blocks of multivariate time series. Especially, spectral BGC and conditional spectral BGC is used to disclose blockwise causal flow among different brain areas in variant frequencies. In this paper, we demonstrate that (i) BGC in time domain may not disclose true causality at all. (ii) Due to the use of the transfer function or its inverse matrix and partial information of the multivariate linear regression model, both of spectral BGC and conditional spectral BGC have shortcomings and/or limitations which may inevitably lead to misinterpretation results. We then in time and frequency domains develop two new multivariate causality methods for the multivariate linear regression model, called blockwise new causality (BNC) and spectral BNC respectively. By several examples we confirm that BNC measures are more reasonable and understandable than BGC or conditional BGC. Finally, for EEG data from an epilepsy patient we analyze event-related potential (ERP) causality and demonstrate that both of BGC and BNC methods show significant causality flow in frequency domain, but the spectral BNC method yields satisfactory and convincing result which is consistent with event-related time-frequency power spectrum activity. The spectral BGC method is shown to generate misleading results.