Large Price Changes and Pervasive Non-Linearity in Financial Markets : Implications and Interpretations

We show that expected returns on US stocks and all major stock world market indices are non-linearly dependent on previous returns. The expected sign of returns tends to reverse after large price movements and trends tend to continue after small movements. This property can be captured by a simple polynomial model. Incorrectly fitting a simple linear model to the data leads to substantial bias in coefficient estimates and the polynomial model can be used to eliminate trends in the data. In addition, well known technical trading rules may be substantially driven by the non-linear behavior observed