Extracting Information on Flow Direction in Multivariate Time Series

Phase slope index is a measure which aims at detecting causal relation of interdependence in multivariate time series. One drawback of this approach relies in its incapability to distinguish the direct and indirect relations. So, in order to identify only direct relations, we propose to replace the ordinary coherence function used in the phase slope index with the partial coherence. Furthermore, 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. In order to cope with the difficult issue of bidirectional flow, which cannot be addressed by the coherence based phase slope index, we propose another index based on the directed transfer function. Experimental results support the relevance of the new indices, both based on autoregressive modeling, in multivariate time series.