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Assessing Dynamic Spectral Causality 
by Lagged Adaptive Directed Transfer 
Function and Instantaneous Effect 
Factor 
It is of significance to assess the dynamic spectral causality among physiological signals. 
Several practical estimators adapted from spectral Granger causality have been exploited to 
track dynamic causality based on the framework of time-varying multivariate autoregressive 
(tvMVAR) models. The nonzero covariance of the model's residuals has been used to 
describe the instantaneous effect phenomenon in some causality estimators. However, for 
the situations with Gaussian residuals in some autoregressive models, it is challenging to 
distinguish the directed instantaneous causality if the sufficient prior information about the 
“causal ordering” is missing. Here, we propose a new algorithm to assess the time-varying 
causal ordering of tvMVAR model under the assumption that the signals follow the same 
acyclic causal ordering for all time lags and to estimate the instantaneous effect factor (IEF) 
value in order to track the dynamic directed instantaneous connectivity. The time-lagged 
adaptive directed transfer function (ADTF) is also estimated to assess the lagged causality 
after removing the instantaneous effect. In this study, we first investigated the performance 
of the causal-ordering estimation algorithm and the accuracy of IEF value. Then, we 
presented the results of IEF and time-lagged ADTF method by comparing with the 
conventional ADTF method through simulations of various propagation models. Statistical 
analysis results suggest that the new algorithm could accurately estimate the causal 
ordering and give a good estimation of the IEF values in the Gaussian residual conditions. 
Meanwhile, the time-lagged ADTF approach is also more accurate in estimating the time-lagged 
dynamic interactions in a complex nervous system after extracting the instantaneous 
effect. In addition to the simulation studies, we applied the proposed method to estimate the
dynamic spectral causality on real visual evoked potential (VEP) data in a human subject. 
Its usefu- ness in time-variant spectral causality assessment was demonstrated through the 
mutual causality investigation of brain activity during the VEP experiments.

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Assessing dynamic spectral causality by lagged adaptive directed transfer function and instantaneous effect factor

  • 1. Assessing Dynamic Spectral Causality by Lagged Adaptive Directed Transfer Function and Instantaneous Effect Factor It is of significance to assess the dynamic spectral causality among physiological signals. Several practical estimators adapted from spectral Granger causality have been exploited to track dynamic causality based on the framework of time-varying multivariate autoregressive (tvMVAR) models. The nonzero covariance of the model's residuals has been used to describe the instantaneous effect phenomenon in some causality estimators. However, for the situations with Gaussian residuals in some autoregressive models, it is challenging to distinguish the directed instantaneous causality if the sufficient prior information about the “causal ordering” is missing. Here, we propose a new algorithm to assess the time-varying causal ordering of tvMVAR model under the assumption that the signals follow the same acyclic causal ordering for all time lags and to estimate the instantaneous effect factor (IEF) value in order to track the dynamic directed instantaneous connectivity. The time-lagged adaptive directed transfer function (ADTF) is also estimated to assess the lagged causality after removing the instantaneous effect. In this study, we first investigated the performance of the causal-ordering estimation algorithm and the accuracy of IEF value. Then, we presented the results of IEF and time-lagged ADTF method by comparing with the conventional ADTF method through simulations of various propagation models. Statistical analysis results suggest that the new algorithm could accurately estimate the causal ordering and give a good estimation of the IEF values in the Gaussian residual conditions. Meanwhile, the time-lagged ADTF approach is also more accurate in estimating the time-lagged dynamic interactions in a complex nervous system after extracting the instantaneous effect. In addition to the simulation studies, we applied the proposed method to estimate the
  • 2. dynamic spectral causality on real visual evoked potential (VEP) data in a human subject. Its usefu- ness in time-variant spectral causality assessment was demonstrated through the mutual causality investigation of brain activity during the VEP experiments.