In this paper we consider tests for nonlinear time series, which are
motivated by the notion of serial dependence. The proposed tests are based on
comparisons with the quantile spectral density, which can be considered as a
quantile version of the usual spectral density function. The quantile spectral
density 'measures' sequential dependence structure of a time series, and is
well defined under relatively weak mixing conditions. We propose an estimator
for the quantile spectral density and derive its asympototic sampling
properties. We use the quantile spectral density to construct a goodness of fit
test for time series and explain how this test can also be used for comparing
the sequential dependence structure of two time series. The method is
illustrated with simulations and some real data examples