Comparative analysis of parameter estimation methods for stable distributions applied to commodity markets

Bakary D. Coulibaly; Siba Kalivogui; Aguemon Wiwegnon Uriel-Longin; Marcel Sihintoe Badiane; Chaibi Ghizlane; Nouhan Traoré; Bakary D. Coulibaly; Siba Kalivogui; Aguemon Wiwegnon Uriel-Longin; Marcel Sihintoe Badiane; Chaibi Ghizlane; Nouhan Traoré

doi:10.3934/InnoEcon.2026002

Innovation Economics

2026, Volume 1, Issue 1: 34-51. doi: 10.3934/InnoEcon.2026002

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Research article

Comparative analysis of parameter estimation methods for stable distributions applied to commodity markets

1.
Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea
2.
Department of Mathematics, Laboratory of Modeling and Mathematical Structures, Sidi Mohamed Ben Abdellah University, Route d'Imouzzer, 30000 Fez, Morocco

Received: 01 January 2026 Revised: 17 June 2026 Accepted: 23 June 2026 Published: 29 June 2026
JEL Codes: C10, C13, C15, C16, G10

This work presents a comparative analysis of the three main methods for estimating the parameters of stable distributions: McCulloch, Koutrouvelis and the maximum likelihood estimator applied to the returns of gold, silver, and uranium prices. The analysis focuses on four complementary dimensions: the estimation bias, the average quadratic error, the average absolute error, and the execution time. The results highlight the trade-offs between statistical precision and computational complexity for each method. This study provides practical recommendations for selecting an estimation method tailored to the unique characteristics of raw material markets.
- stable distribution,
- $ \alpha $-stable,
- parameter estimation,
- raw materials,
- gold,
- uranium,
- comparison methods,
- performance evaluation
Citation: Bakary D. Coulibaly, Siba Kalivogui, Aguemon Wiwegnon Uriel-Longin, Marcel Sihintoe Badiane, Chaibi Ghizlane, Nouhan Traoré. Comparative analysis of parameter estimation methods for stable distributions applied to commodity markets[J]. Innovation Economics, 2026, 1(1): 34-51. doi: 10.3934/InnoEcon.2026002

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Abstract

This work presents a comparative analysis of the three main methods for estimating the parameters of stable distributions: McCulloch, Koutrouvelis and the maximum likelihood estimator applied to the returns of gold, silver, and uranium prices. The analysis focuses on four complementary dimensions: the estimation bias, the average quadratic error, the average absolute error, and the execution time. The results highlight the trade-offs between statistical precision and computational complexity for each method. This study provides practical recommendations for selecting an estimation method tailored to the unique characteristics of raw material markets.

References

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