Consistent Measures of Dependence as a Tool of Eliciting Non-linear Features in Complex Systems (Mildly Formalized System Identification)
The paper presents an approach to the input/output system identification under the condition that no analytical model representation of the system is assumed to be known. Within the approach, the key issue of the problem is a proper handling of inherent dependence between the input and output variables of the system. Using a consistent measure of stochastic dependence of random processes has been proposed within the identification scheme. The measure of dependence is the maximal correlation function. It properly reflects actual nonlinear dependence between random processes, while those of based on the dispersion and, moreover, ordinary product correlation functions do not. In addition, the measure directly leads to determining the input/output relationship of the investigated system. Within the approach, a degree of the system nonlinearity based on the maximal correlation is proposed.