 Analysis of threshold Ornstein–Uhlenbeck process with piecewise linear drift and piecewise constant diffusionDingwen Zhang and Zhuowei Sun Chaos, Solitons & Fractals, 2025, vol. 199, issue P2 Abstract: The threshold Ornstein−Uhlenbeck process is a stochastic process defined by a stochastic differential equation, with a piecewise linear drift term and a piecewise constant diffusion term. We address the problem of estimating the drift and diffusion parameters along with the thresholds. To solve this problem, we propose two algorithms, LS&MQV&S and LS&QV&S, which incorporate the least squares method for the drift parameters, the modified quadratic variation and quadratic variation methods for the diffusion parameters, a testing procedure to determine the presence of additional drift- or diffusion-thresholds, and a sequential method for the values of the drift- and diffusion-thresholds. Monte Carlo simulation results are presented to illustrate and support our theoretical conclusions. We apply the process to model the U.S. Treasury rates and the currency foreign exchange rates, using the LS&QV&S algorithm to estimate the term structures of the drift and diffusion terms. Keywords: Threshold Ornstein–Uhlenbeck process; Piecewise linear drift term; Piecewise constant diffusion term; Least squares method; Quadratic variation method; Sequential method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925006721 DOI: 10.1016/j.chaos.2025.116659 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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