The art of fitting financial time series with Levy stable distributions

This paper illustrates a procedure for fitting financial data with a-stable distributions. After using all the available methods to evaluate the distribution parameters, one can qualitatively select the best estimate and run some goodness-of-fit tests on this estimate, in order to quantitatively assess its quality. It turns out that, for the two investigated data sets (MIB30 and DJIA from 2000 to present), an a-stable fit of log-returns is reasonably good.