The sample autocorrelation function of non-linear time series

When studying a real-life time series, it is frequently reasonable to assume, possibly after a suitable transformation, that the data come from a stationary time series (Xt). This means that the finite-dimensional distributions of this sequence are invariant under shifts of time. Various stationary time series models have been studied in detail in the literature. A standard assumption is that the time series is Gaussian or, more generally, that it has a probability distribution with light tails, in the sense that P(lXtl > x) decays to zero at least exponentially. Zie: Summary