Modelling DAX by applying parabola approximation method

Abstract

Existing studies indicate that the nonlinear phenomenon occurs in the movement of stock prices (or returns) but few models provide the adequate explanations. We apply 'parabola approximation' as an inclusion of nonlinear explanatory variable to model German Deutscher Aktien IndeX (DAX) closing prices during 2 January 2006 to 12 June 2013. The empirical result shows accurate fits which means the model applied characterises DAX appropriately. As a result, the coefficients of the model meaningfully determine the movement of DAX. After examining the coefficients, unusual changes of the coefficients as a sign of approaching fluctuations in the DAX prices display right before the announcement of the bankruptcy of Lehman Brothers. In this way, we provide an instrument to detect the prompt structural changes and risks of the financial market.