Detecting and evaluating intrinsic nonlinearity present in the mutual dependence between two variables

Detection and evaluation of intrinsic nonlinearity present in the mutual dependence between two variables is an important subject that is faced in many situations such as the identification of a system based on the relationship between input and output signals. We propose a method for detecting and evaluating the intrinsic nonlinearity without requiring a long data series. This method is based on comparing the mutual information between the original data series with that between new ones obtained by removing linear dependence from the original ones. The point is to remove linear dependence from the original data and to effectively compute mutual information even for relatively short data. We apply the method to several sample data and confirm the effectiveness of the method. We also discuss its applicability to causality analysis.