Determining the flow direction of causal interdependence in multivariate time series

Phase slope index is a measure which can detect causal direction of interdependence in multivariate time series. However, this coherence based method may not distinguish between direct and indirect relations from one time series to another one acting through a third time series. So, in order to identify only direct relations, we propose to replace the ordinary coherence function used in phase slope index with the partial coherence. In a second step, we consider and compare two estimators of the coherence functions, the first one based on Fourier transform and the second one on an autoregressive model. These measures are tested and compared with Granger causality index on linear and non linear time series. Experimental results support the relevance of the new index including partial coherence based on autoregressive modelling in multivariate time series.