Frequency Domain Causality Analysis Method for Multivariate Systems in Hypothesis Testing Framework

摘要

A variety of causality analysis methods have been proposed and used for complex large multivariate systems. In the frequency domain, partial directed coherence (PDC) is an important method. We expect that the frequency domain methods can provide a more detailed explanation of causal influence over different frequencies, but PDC provides no quantitative information to quantify the causal strength and the interpretation of causality over a specific frequency is still unexplained. Based on the statistical property of the renormalized PDC, a frequency domain causality analysis method in the hypothesis testing framework is employed in this paper to resolve these issues. In order to achieve a lower computational load, another method with a simpler definition is proposed. The interpretations of causal strength given by these two methods are shown to be consistent with that given by Granger causality, and the frequency distribution is reasonable and informative. Several simulation examples are demonstrated to illustrate the performance of these two methods.