Log-Moment Estimators for the Generalized Linnik and Mittag-Leffler Distributions with Applications to Financial Modeling
- 1 University of Houston-Downtown, United States
- 2 Case Western Reserve University, United States
Abstract
We propose formal estimation procedures for the parameters of the generalized, heavy-tailed three-parameter Linnik gL(α, µ, δ) and Mittag-Leffler gML(α, µ, δ) distributions. The paper also aims to provide guidance about the different inference procedures for the different two-parameter Linnik and Mittag-Leffler distributions in the current literature. 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 two-parameter Linnik and Mittag-Leffler models are not flexible enough to accurately model the current stock market data.
DOI: https://doi.org/10.3844/jmssp.2018.156.166
Copyright: © 2018 Dexter O. Cahoy and Wojbor A. Woyczyński. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Linnik
- Mittag-Leffler
- Heavy-Tailed
- Dow Jones
- S&P500
- Finance
- Parameter Estimation