Entropy testing for nonlinearity in time series

In this paper we 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 [1], 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 [2]. 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. [1] Granger C. W., Maasoumi E., and Racine J. (2004) "A dependence metric for possibly nonlinear processes", Journal of Time Series Analysis, 25, 5: 649-669. [2] Schreiber T. and Schmitz A. (2000) "Surrogate time series", Physica D, 142: 346-382.