Abstract
Akaike's Noise Contribution Ratio (NCR) has been used for the analysis of causality of two-variable settings of biological time series in Neuroscience. In contrast to the conventional correlation definition, this methodology is able to detect the direction of the influence between two variables. However, if a third series intervention is taken into account, the validity of causality is questionable, since possible feedback with third series can induce spurious or indirect causality. In this paper, we introduce a modification to NCR that accounts for partial directed causality for the case of more than two variables (pNCR). We also extend this methodology for the case of non-stationary time series by means of the use of the sliding windows technique, which provides a time-frequency approach. This methodology produces a 2D matrix (time and frequency) of pNCR coefficients, which is difficult to interpret and visualize. To facilitate the visualization and interpretation of the pNCR for the case of non-stationary time series, we summarize the information of the spectrum of the pNCR as the area under the curve (pNCA), which projects this 2D matrix into the 1D space (a vector of coefficients), which shows the time course rate of influence from one variable to another in both directions.
