A set of novel correlation tests for nonlinear system variables

A set of novel correlation tests using omni-directional cross-correlation functions (ODCCFs), which are based on the first order cross-correlation functions (CCF), are proposed in the present study to comprehensively detect nonlinear relationships between variables. Then the ODCCFs are combined into a set of concise formulations to provide better illustration of detected correlations and reduce the number of correlation plots. Compared to the other approaches, the new methodology brings much more power in detection of nonlinear correlations. The efficiency and effectiveness of the new algorithm are demonstrated through simulation studies and comparisons with other linear and nonlinear correlation tests. The results can be widely applied in many relevant fields.