Financial time series

Abstract

The evolution of financial markets is a complicated real-world phenomenon that ranks at the top in terms of difficulty of modeling and/or prediction. One reason for this difficulty is the well-documented nonlinearity that is inherent at work. The state-of-the-art on the nonlinear modeling of financial returns is given by the popular auto-regressive conditional heteroscedasticity (ARCH) models and their generalizations but they all have their short-comings. Foregoing the goal of finding the 'best' model, it is possible to simply transform the problem into a more manageable setting such as the setting of linearity. The form and properties of such a transformation are given, and the issue of one-step-ahead prediction using the new approach is explicitly addressed. © 2009 John Wiley & Sons, Inc.