An entropy based test for non-linear dependence in time series

The aim of the paper is to propose a novel 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, possessing many desirable properties, together with a suitable extension of surrogate data methods, a class of Monte Carlo based tests introduced with the aim of building consistent tests for nonlinearity without making distributional assumptions on the test statistics. The use of parametric bootstrap methods is also investigated. In this paper we show how the test can be employed in order to detect the lags at which a significant nonlinear relationship is expected in the same fashion as the autocorrelation function is used for linear processes. The power and size of the test is assessed through simulation studies.