Can the stock market be linearised?

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 inherently at work. The state-of-the-art on the nonlinear modeling of financial returns is given by the popular ARCH (Auto-Regressive Conditional Heteroscedasticity) models and their generalisations but they all have their short-comings. Foregoing the goal of finding the ‘best’ model, we propose an exploratory, model-free approach in trying to understand this difficult type of data. In particular, we propose to 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.