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The art of fitting financial time series with Levy stable distributions

Enrico Scalas·Kyungsik Kim
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Abstract

This paper illustrates a procedure for fitting financial data with $α$-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 $α$-stable fit of log-returns is reasonably good.

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Enrico Scalas, Kyungsik Kim. 2006-08-23. The art of fitting financial time series with Levy stable distributions. https://arxiv.org/abs/physics/0608224

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