{"title":"用模糊聚类检测马尔可夫切换模型的状态数","authors":"Edoardo Otranto, Luca Scaffidi Domianello","doi":"10.1007/s10479-025-06585-w","DOIUrl":null,"url":null,"abstract":"<div><p>An open problem of Markov switching models is identifying the number of states, generally fixed a priori; it is impossible to apply classical tests due to the issue of the nuisance parameters present only under the alternative hypothesis. In this work, we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to identify the number of states in this framework. The procedure is very simple to apply, considering that it is performed independently of the data generating process and that the indicators we use are available in most statistical packages. Furthermore, the proposed approach appears to be sufficiently robust to perturbations in the data generating processes. A final application of real data completes the analysis.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1855 - 1890"},"PeriodicalIF":4.5000,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10479-025-06585-w.pdf","citationCount":"0","resultStr":"{\"title\":\"On using fuzzy clustering for detecting the number of states in Markov switching models\",\"authors\":\"Edoardo Otranto, Luca Scaffidi Domianello\",\"doi\":\"10.1007/s10479-025-06585-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>An open problem of Markov switching models is identifying the number of states, generally fixed a priori; it is impossible to apply classical tests due to the issue of the nuisance parameters present only under the alternative hypothesis. In this work, we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to identify the number of states in this framework. The procedure is very simple to apply, considering that it is performed independently of the data generating process and that the indicators we use are available in most statistical packages. Furthermore, the proposed approach appears to be sufficiently robust to perturbations in the data generating processes. A final application of real data completes the analysis.</p></div>\",\"PeriodicalId\":8215,\"journal\":{\"name\":\"Annals of Operations Research\",\"volume\":\"349 3\",\"pages\":\"1855 - 1890\"},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2025-05-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10479-025-06585-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10479-025-06585-w\",\"RegionNum\":3,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06585-w","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
On using fuzzy clustering for detecting the number of states in Markov switching models
An open problem of Markov switching models is identifying the number of states, generally fixed a priori; it is impossible to apply classical tests due to the issue of the nuisance parameters present only under the alternative hypothesis. In this work, we show, by Monte Carlo simulations, that fuzzy clustering is able to reproduce the parametric state inference derived from the Hamilton filter and that the typical indices used in clustering to determine the number of groups can be used to identify the number of states in this framework. The procedure is very simple to apply, considering that it is performed independently of the data generating process and that the indicators we use are available in most statistical packages. Furthermore, the proposed approach appears to be sufficiently robust to perturbations in the data generating processes. A final application of real data completes the analysis.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.