A Powerful Entropy Test for “linearity” against Nonlinearity in Time Series

In this paper we investigate a test for the identification of nonlinear dependence in time series against more general “nulls” than mere “independence”. The approach is based on a combination of an entropy dependence metric, possessing many desirable properties and used as a test statistic, together with a suitable extension of surrogate data methods, a class of Monte Carlo based tests introduced with the aim of building consistent distributionfree tests for nonlinearity. The use of 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. We discuss some theoretical aspects related to the entropy measure and its estimators. The power and size of the test is assessed through simulation studies; applications to well known real data are also presented.