The art of fitting financial time series with Levy stable distributions
This paper illustrates a procedure for fitting financial data with $\alpha$-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 $\alpha$-stable fit of log-returns is reasonably good.
References listed on IDEAS
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- Rafal Weron, 2001.
"Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime,"
HSC Research Reports
HSC/01/01, Hugo Steinhaus Center, Wroclaw University of Technology.
- Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index > 2 Does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
- Rafal Weron, 2003. "Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime," Econometrics 0305003, EconWPA.
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- Benoit Mandelbrot, 1963.
"The Variation of Certain Speculative Prices,"
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- Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
- Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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