We propose a test for identification of nonlinear serial dependence in time series against the 15 general "null" of linearity, in contrast to the more widely examined null of "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 i) a suitable extension of surrogate data methods, a class of Monte Carlo distribution-free tests for nonlinearity; and ii) the use of a smoothed sieve bootstrap scheme. We show how the tests can be employed to detect the lags at which a 20 significant nonlinear relationship is expected in the same fashion as the autocorrelation function is used for linear models. We prove the asymptotic validity of the procedures proposed and of the corresponding inferences. The small sample size performance of the tests is assessed through a simulation study. Applications to real data sets of different kinds are also presented.
