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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. [ABSTRACT FROM PUBLISHER]

In this paper we first point out a fatal drawback that the widely used Granger causality (GC) needs to estimate the autoregressive model, which is equivalent to taking a series of backward recursive operations which are infeasible in many irreversible chemical reaction models. Thus, new causality (NC) proposed by Hu et al. (2011) is theoretically shown to be more sensitive to reveal true causality than GC. We then apply GC and NC to motor imagery (MI) which is an important mental process in cognitive neuroscience and psychology and has received growing attention for a long time. We study causality flow during MI using scalp electroencephalograms from nine subjects in Brain–computer interface competition IV held in 2008. We are interested in three regions: Cz (central area of the cerebral cortex), C3 (left area of the cerebral cortex), and C4 (right area of the cerebral cortex) which are considered to be optimal locations for recognizing MI states in the literature. Our results show that: 1) there is strong directional connectivity from Cz to C3/C4 during left- and right-hand MIs based on GC and NC; 2) during left-hand MI, there is directional connectivity from C4 to C3 based on GC and NC; 3) during right-hand MI, there is strong directional connectivity from C3 to C4 which is much clearly revealed by NC than by GC, i.e., NC largely improves the classification rate; and 4) NC is demonstrated to be much more sensitive to reveal causal influence between different brain regions than GC. [ABSTRACT FROM PUBLISHER]