{"title":"时间非均匀Ornstein-Uhlenbeck过程的参数最小二乘估计","authors":"G. Pramesti","doi":"10.1515/mcma-2022-2127","DOIUrl":null,"url":null,"abstract":"Abstract We address the least-squares estimation of the drift coefficient parameter θ = ( λ , A , B , ω p ) \\theta=(\\lambda,A,B,\\omega_{p}) of a time-inhomogeneous Ornstein–Uhlenbeck process that is observed at high frequency, in which the discretized step size ℎ satisfies h → 0 h\\to 0 . In this paper, under the conditions n h → ∞ nh\\to\\infty and n h 2 → 0 nh^{2}\\to 0 , we prove the consistency and the asymptotic normality of the estimators. We obtain the convergence of the parameters at rate n h \\sqrt{nh} , except for ω p \\omega_{p} at n 3 h 3 \\sqrt{n^{3}h^{3}} . To verify our theoretical findings, we do a simulation study. We then illustrate the use of the proposed model in fitting the energy use of light fixtures in one Belgium household and the stock exchange.","PeriodicalId":46576,"journal":{"name":"Monte Carlo Methods and Applications","volume":"29 1","pages":"1 - 32"},"PeriodicalIF":0.8000,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process\",\"authors\":\"G. Pramesti\",\"doi\":\"10.1515/mcma-2022-2127\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We address the least-squares estimation of the drift coefficient parameter θ = ( λ , A , B , ω p ) \\\\theta=(\\\\lambda,A,B,\\\\omega_{p}) of a time-inhomogeneous Ornstein–Uhlenbeck process that is observed at high frequency, in which the discretized step size ℎ satisfies h → 0 h\\\\to 0 . In this paper, under the conditions n h → ∞ nh\\\\to\\\\infty and n h 2 → 0 nh^{2}\\\\to 0 , we prove the consistency and the asymptotic normality of the estimators. We obtain the convergence of the parameters at rate n h \\\\sqrt{nh} , except for ω p \\\\omega_{p} at n 3 h 3 \\\\sqrt{n^{3}h^{3}} . To verify our theoretical findings, we do a simulation study. We then illustrate the use of the proposed model in fitting the energy use of light fixtures in one Belgium household and the stock exchange.\",\"PeriodicalId\":46576,\"journal\":{\"name\":\"Monte Carlo Methods and Applications\",\"volume\":\"29 1\",\"pages\":\"1 - 32\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monte Carlo Methods and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/mcma-2022-2127\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monte Carlo Methods and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/mcma-2022-2127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
摘要
摘要我们讨论了在高频下观测到的时间非均匀Ornstein–Uhlenbeck过程的漂移系数参数θ=(λ,A,B,ωp)\θ=(\lambda,A,B,\omega_{p})的最小二乘估计,其中离散化的步长ℎ 满足h→ 0小时\到0。在本文中,在条件n h→ ∞ nh\to\infty和n h 2→ 0nh^{2}\到0,我们证明了估计量的一致性和渐近正态性。我们得到了在速率n h \sqrt{nh}下参数的收敛性,除了ω^{3}h^{3} }。为了验证我们的理论发现,我们进行了一项模拟研究。然后,我们说明了所提出的模型在拟合比利时一个家庭和证券交易所的灯具能源使用方面的用途。
Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process
Abstract We address the least-squares estimation of the drift coefficient parameter θ = ( λ , A , B , ω p ) \theta=(\lambda,A,B,\omega_{p}) of a time-inhomogeneous Ornstein–Uhlenbeck process that is observed at high frequency, in which the discretized step size ℎ satisfies h → 0 h\to 0 . In this paper, under the conditions n h → ∞ nh\to\infty and n h 2 → 0 nh^{2}\to 0 , we prove the consistency and the asymptotic normality of the estimators. We obtain the convergence of the parameters at rate n h \sqrt{nh} , except for ω p \omega_{p} at n 3 h 3 \sqrt{n^{3}h^{3}} . To verify our theoretical findings, we do a simulation study. We then illustrate the use of the proposed model in fitting the energy use of light fixtures in one Belgium household and the stock exchange.