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Parameter estimation and random number generation for student Lévy processes

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  • Li, Shuaiyu
  • Wu, Yunpei
  • Cheng, Yuzhong

Abstract

To address the challenges in estimating parameters of the widely applied Student-Lévy process, the study introduces two distinct methods: a likelihood-based approach and a data-driven approach. A two-step quasi-likelihood-based method is initially proposed, countering the non-closed nature of the Student-Lévy process's distribution function under convolution. This method utilizes the limiting properties observed in high-frequency data, offering estimations via a quasi-likelihood function characterized by asymptotic normality. Additionally, a novel neural-network-based parameter estimation technique is advanced, independent of high-frequency observation assumptions. Utilizing a CNN-LSTM framework, this method effectively processes sparse, local jump-related data, extracts deep features, and maps these to the parameter space using a fully connected neural network. This innovative approach ensures minimal assumption reliance, end-to-end processing, and high scalability, marking a significant advancement in parameter estimation techniques. The efficacy of both methods is substantiated through comprehensive numerical experiments, demonstrating their robust performance in diverse scenarios.

Suggested Citation

  • Li, Shuaiyu & Wu, Yunpei & Cheng, Yuzhong, 2024. "Parameter estimation and random number generation for student Lévy processes," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:csdana:v:194:y:2024:i:c:s0167947324000173
    DOI: 10.1016/j.csda.2024.107933
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    References listed on IDEAS

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    1. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    2. Nicola Cufaro Petroni, 2007. "Mixtures in non stable Levy processes," Papers math/0702058, arXiv.org.
    3. Wang, Xiaolong & Feng, Jing & Liu, Qi & Li, Yongge & Xu, Yong, 2022. "Neural network-based parameter estimation of stochastic differential equations driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    4. Masuda, Hiroki, 2019. "Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 1013-1059.
    5. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.
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