{"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":49992,"journal":{"name":"Journal of the Korean Statistical Society","volume":"50 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Statistical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s42952-023-00247-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","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.
期刊介绍：
The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.
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