M. D. Márquez1
Modelling financial time series is a field in constant growth, as much from a theoretical point of view as from estimation algorithms development. Under linearity hypothesis, Box and Jenkins methodology for ARIMA models, provides a well developed statistical theory and computational tools which are readily available. But financial time series exhibit some features that cannot be described by linear time series models; this situation has motivated many authors to consider non linear alternatives. In this lecture we present the distributional and empirical properties of the most commonly used non linear models in variance (ARCH, GARCH and SV), non linear models in mean (Bilinear and TAR) and the new developments that allow to capture both forms of non linearity. Finally, applications to real data sets are presented.