Log-moment estimators for the generalized Linnik and Mittag-Leffler distributions with applications to financial modeling
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We propose formal estimation procedures for the parameters of the generalized, three-parameter Linnik gL(α,μ, δ) and Mittag-Leffler gML(α,μ, δ) 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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