Non-linear time series models

The last three decades have seen quite dramatic changes the way we modeled time dependent data. Linear processes have been in the center stage in modeling time series. As far as the second order properties are concerned, the theory and the methodology are very adequate.However, there are more and more evidences that linear models are not sufficiently flexible and rich enough for modeling purposes and that failure to account for non-linearities can be very misleading and have undesired consequences.