Assessing the strength of directed influences among neural signals using renormalized partial directed coherence

Partial directed coherence is a powerful tool used to analyze interdependencies in multivariate systems based on vector autoregressive modeling. This frequency domain measure for Granger-causality is designed such that it is normalized to [0,1]. This normalization induces several pitfalls for the interpretability of the ordinary partial directed coherence, which will be discussed in some detail in this paper. In order to avoid these pitfalls, we introduce renormalized partial directed coherence and calculate confidence intervals and significance levels. The performance of this novel concept is illustrated by application to model systems and to electroencephalography and electromyography data from a patient suffering from Parkinsonian tremor.