{"title":"A criterion for estimating the largest linear homoscedastic zone in Gaussian data","authors":"Jean-Marc Bardet","doi":"10.1016/j.jspi.2024.106223","DOIUrl":null,"url":null,"abstract":"<div><p>A criterion is constructed to identify the largest homoscedastic region in a Gaussian dataset. This can be reduced to a one-sided non-parametric break detection, knowing that up to a certain index the output is governed by a linear homoscedastic model, while after this index it is different (<em>e.g.</em> a different model, different variables, different volatility, ….). We show the convergence of the estimator of this index, with asymptotic concentration inequalities that can be exponential. A criterion and convergence results are derived when the linear homoscedastic zone is bounded by two breaks on both sides. Additionally, a criterion for choosing between zero, one, or two breaks is proposed. Monte Carlo experiments will also confirm its very good numerical performance.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375824000806","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A criterion is constructed to identify the largest homoscedastic region in a Gaussian dataset. This can be reduced to a one-sided non-parametric break detection, knowing that up to a certain index the output is governed by a linear homoscedastic model, while after this index it is different (e.g. a different model, different variables, different volatility, ….). We show the convergence of the estimator of this index, with asymptotic concentration inequalities that can be exponential. A criterion and convergence results are derived when the linear homoscedastic zone is bounded by two breaks on both sides. Additionally, a criterion for choosing between zero, one, or two breaks is proposed. Monte Carlo experiments will also confirm its very good numerical performance.