Correntropy as a Novel Measure for Nonlinearity Tests

Statistical tests have become an essential step in nonlinear system modeling due to the complexities involved in their analysis. Correntropy is a kernel-based similarity measure which includes the information of both distribution and time structure of a stochastic process. The correntropy function´s capability of preserving nonlinear characteristics and high order moments makes it a suitable candidate as a statistic for determining whether a nonlinear structure exists within the system that created the observed time series. Experiments based on surrogate data methods have confirmed that correntropy can be employed as a discriminant measure for detecting nonlinear characteristics in time series.