Shortcomings/Limitations of Blockwise Granger Causality and Advances of Blockwise New Causality

Multivariate blockwise Granger causality (BGC) is used to reflect causal interactions among blocks of multivariate time series. In particular, spectral BGC and conditional spectral BGC are used to disclose blockwise causal flow among different brain areas in various frequencies. In this paper, we demonstrate that: 1) BGC in time domain may not necessarily disclose true causality and 2) 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. We then, in time and frequency domains, develop two new multivariate blockwise causality methods for the linear regression model called blockwise new causality (BNC) and spectral BNC, respectively. By several examples, we confirm that BNC measures are more reasonable and sensitive to reflect true causality or trend of true causality than BGC or conditional BGC. Finally, for electroencephalograph data from an epilepsy patient, we analyze event-related potential causality and demonstrate that both of the BGC and BNC methods show significant causality flow in frequency domain, but the spectral BNC method yields satisfactory and convincing results, which are consistent with an event-related time-frequency power spectrum activity. The spectral BGC method is shown to generate misleading results. Thus, we deeply believe that our new blockwise causality definitions as well as our previous NC definitions may have wide applications to reflect true causality among two blocks of time series or two univariate time series in economics, neuroscience, and engineering.