时间非均匀Ornstein-Uhlenbeck过程的参数最小二乘估计

IF 0.8 Q3 STATISTICS & PROBABILITY
G. Pramesti
{"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":null,"pages":null},"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\":null,\"pages\":null},\"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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信