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arXiv · 1803.11459

Log-moment estimators for the generalized Linnik and Mittag-Leffler distributions with applications to financial modeling

Dexter O. Cahoy·Wojbor A. Woyczyński
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Abstract

We propose formal estimation procedures for the parameters of the generalized, three-parameter Linnik $gL(\alpha,\mu, \delta)$ and Mittag-Leffler $gML(\alpha,\mu, \delta)$ distributions. The estimators are derived from the moments of the log-transformed random variables, and are shown to be asymptotically unbiased. The estimation algorithms are computationally efficient and the proposed procedures are tested using the daily S\&P 500 and Dow Jones index data. The results show that the standard two-parameter Linnik and Mittag-Leffler models are not flexible enough to accurately model the current stock market data.

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Dexter O. Cahoy, Wojbor A. Woyczyński. 2018-03-30. Log-moment estimators for the generalized Linnik and Mittag-Leffler distributions with applications to financial modeling. https://arxiv.org/abs/1803.11459

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