{"title":"Sequential online monitoring for autoregressive time series of counts","authors":"","doi":"10.1007/s42952-023-00247-y","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This study considers the online monitoring problem for detecting the parameter change in time series of counts. For this task, we construct a monitoring process based on the residuals obtained from integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models. We consider this problem within a more general framework using martingale difference sequences as the monitoring problem on GARCH-type processes based on the residuals or score vectors can be viewed as a special case of the monitoring problems on martingale differences. The limiting behavior of the stopping rule is investigated in this general set-up and is applied to the INGARCH processes. To assess the performance of our method, we conduct Monte Carlo simulations. A real data analysis is also provided for illustration. Our findings in this empirical study demonstrate the validity of the proposed monitoring process.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-023-00247-y","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
This study considers the online monitoring problem for detecting the parameter change in time series of counts. For this task, we construct a monitoring process based on the residuals obtained from integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models. We consider this problem within a more general framework using martingale difference sequences as the monitoring problem on GARCH-type processes based on the residuals or score vectors can be viewed as a special case of the monitoring problems on martingale differences. The limiting behavior of the stopping rule is investigated in this general set-up and is applied to the INGARCH processes. To assess the performance of our method, we conduct Monte Carlo simulations. A real data analysis is also provided for illustration. Our findings in this empirical study demonstrate the validity of the proposed monitoring process.
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