Testing for nonlinear serial dependence in time series with surrogate data and entropy measures

In this work we propose a nonparametric test for the identification of nonlinear dependence in time series. The approach is based on a combination of a test statistic based on an entropy dependence metric together with a suitable extension of surrogate data methods, a class of Monte Carlo tests introduced in the field of nonlinear dynamics. We focus on the null hypothesis of linear Gaussian processes and we derive the asymptotic theory for the test statistics. Since the asymptotic approximations depend on unknown quantities and require long series to be feasible we advocate the use of surrogate methods. We prove the asymptotic validity of the inference derived from the test and show the finite sample performance through a small simulation study.