Threshold Models for Lévy Processes and Approximate Maximum Likelihood Estimation

Using the Lévy process (solution of the Ito–Skorokhod stochastic differential equation), we propose the structure of the model of a threshold process and an approximate maximum likelihood method based on the approximation of the logarithmic function of the likelihood of observations. We find the est...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2024-03, Vol.60 (2), p.261-267
Main Authors: Tsai, Henghsiu, Nikitin, A. V.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Control
Differential equations
Levy distribution
Likelihood ratio
Mathematics
Mathematics and Statistics
Maximum likelihood estimation
Processor Architectures
Software Engineering/Programming and Operating Systems
Stochastic processes
Systems Theory
Thresholds
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Summary:Using the Lévy process (solution of the Ito–Skorokhod stochastic differential equation), we propose the structure of the model of a threshold process and an approximate maximum likelihood method based on the approximation of the logarithmic function of the likelihood of observations. We find the estimates for the parameters of the two-mode threshold jump process with discretely sampled data and show that it is possible to determine the presence of threshold effects by checking the likelihood ratio.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-024-00666-7