Elimination of third-series effect and defining partial measures of causality

Using the one-way effect extraction method. this paper presents a set of partial causal measures which represents quantitatively the interdependence between a pair of vector-valued processes in the presence of a third process. Those measures are defined for stationary as well as for a class of non-stationary time series. In contrast to conventional conditioning methods, the partial concept defined in the paper would be mostly devoid of feedback distortion by the third process, The paper also discusses statistical inference on the proposed measures.