Scaling properties of financial time series

This thesis will first criticize standard financial theory. The focus will be on return distributions, efficient market hypothesis and the independence of returns. Part two gives the intuition to look at markets in a different view. Namely the one proposed by B. Mandelbrot who has shown that nature itself can often be described with fractals. Then the relationship between fractal power laws and scaling will be explained. The main part focuses on the estimation of the tail index as a scaling parameter with the help of three different techniques: 1. OLS regression on a log-log plot, 2. Hill estimator and 3. the alpha exponent within the stable distribution. In the last section a different power law exponent will be estimated to test for long memory effects (i.e. nonperiodical cycles) in return distributions. The last section gives a conclusion.