{"title":"On strongly dependent zero-inflated INAR(1) processes","authors":"Jan Beran, Frieder Droullier","doi":"10.1007/s00362-023-01496-z","DOIUrl":null,"url":null,"abstract":"Abstract We consider INAR(1) processes modulated by an unobserved strongly dependent $$0-1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results.","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"94 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Papers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00362-023-01496-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We consider INAR(1) processes modulated by an unobserved strongly dependent $$0-1$$ 0-1 process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results.
期刊介绍：
The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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