Modeling Dynamic Regime Shifts in Diffusion Processes: Approximate Maximum Likelihood Estimation for Two-Threshold Ornstein–Uhlenbeck Models

Svajone Bekesiene (), Anatolii Nikitin and Serhii Nechyporuk
Additional contact information
Svajone Bekesiene: Research Group on Logistics and Defence Technology Management, General Jonas Zemaitis Military Academy of Lithuania, Silo 5a, 10322 Vilnius, Lithuania
Anatolii Nikitin: Educational and Scientific Institute of Information Technology and Business, The National University of Ostroh Academy, UA-03580 Ostroh, Ukraine
Serhii Nechyporuk: Department of Economics, The National University of Ostroh Academy, UA-03580 Ostroh, Ukraine

Mathematics, 2025, vol. 13, issue 21, 1-18

Abstract: This study addresses the problem of estimating parameters in a two-threshold Ornstein–Uhlenbeck diffusion process, a model suitable for describing systems that exhibit changes in dynamics when crossing specific boundaries. Such behavior is often observed in real economic and physical processes. The main objective is to develop and evaluate a method for accurately identifying key parameters, including the threshold levels, drift changes, and diffusion coefficient, within this stochastic framework. The paper proposes an iterative algorithm based on approximate maximum likelihood estimation, which recalculates parameter values step by step until convergence is achieved. This procedure simultaneously estimates both the threshold positions and the associated process parameters, allowing it to adapt effectively to structural changes in the data. Unlike previously studied single-threshold systems, two-threshold models are more natural and offer improved applicability. The method is implemented through custom programming and tested using synthetically generated data to assess its precision and reliability. The novelty of this study lies in extending the approximate maximum likelihood framework to a two-threshold Ornstein–Uhlenbeck process and in developing an iterative estimation procedure capable of jointly recovering both threshold locations and regime-specific parameters with proven convergence properties. Results show that the algorithm successfully captures changes in the process dynamics and provides consistent parameter estimates across different scenarios. The proposed approach offers a practical tool for analyzing systems influenced by shifting regimes and contributes to a better understanding of dynamic processes in various applied fields.

Keywords: approximate maximum likelihood method; two-threshold diffusion process; stochastic differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3450/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3450/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3450-:d:1782366

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().