Parsimonious and Efficient Integer-valued Autoregressive Process: Inference and Application

Parsimonious and Efficient Integer-valued Autoregressive Process: Inference and Application | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Parsimonious and Efficient Integer-valued Autoregressive Process: Inference and Application Jiayi Yang, Lianyong Qian, Huaping CHEN This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9064129/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Negative Binomial AutoRegressive-type (NBAR) processes serve as a primary methodological frameworkfor the overdispersed integer-valued time series.However, the factorial terms and the turning parameter inherenting in the probability mass functionrender the model's likelihood function structurally intricate, thereby incurring substantial computational costs.To mitigate this dilemma, a new parsimonious yet efficient integer-valued autoregressive process is proposed,which is specifically built upon the Poisson moment exponential (PME) distribution.As a member of the mixed Poisson family,the PME distribution not only exhibits a more parsimonious structure, but alsoovercomes overdispersionwithout resorting to factorial terms or extra parameters. In this paper, we introduce a class of general PME autoregressive processes, establish their stationarity and ergodicity. For a straightforward illustration of the model's statistical properties, we investigate its linear, approximately linear, and non-linear structural forms.Furthermore, we discuss their conditional maximum likelihood (CML) estimation, establish the asymptotic theory for the CML estimators of the parametersand then analyze their finite-sample behavior by some simulation studies.Last but not least, we validate the outperform of the proposed model by two empirical datasets. Integer-valued time series overdispersion mixed Poisson distribution family autoregressive process CML estimation asymptotic property Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 19 Mar, 2026 Reviewers invited by journal 16 Mar, 2026 Editor assigned by journal 09 Mar, 2026 Submission checks completed at journal 09 Mar, 2026 First submitted to journal 08 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9064129","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606621927,"identity":"a50a4eb0-f1e5-46ed-8ff5-b601b1dc703b","order_by":0,"name":"Jiayi Yang","email":"","orcid":"","institution":"Henan University","correspondingAuthor":false,"prefix":"","firstName":"Jiayi","middleName":"","lastName":"Yang","suffix":""},{"id":606621928,"identity":"8b0047c4-44b3-4a95-a7a6-cf543769f082","order_by":1,"name":"Lianyong Qian","email":"","orcid":"","institution":"Jiangsu Normal University","correspondingAuthor":false,"prefix":"","firstName":"Lianyong","middleName":"","lastName":"Qian","suffix":""},{"id":606621929,"identity":"b81c686d-6160-4fcf-9a6b-30e602d1a333","order_by":2,"name":"Huaping CHEN","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYDACCQYGZiDJwyb/+BhUKIEoLTYy/AxpaSRpSbORbMgxI04L/+zmY48LdxzmMThw5tuDjzsOM/Cz5xgw/NyBx5I7x9KNZ54BajnYu90QyGCQ7HljwNh7BrcWA4kcM2neNqCWw7zbQAwGgxs5BsyMbfi05H+DaDnG80z6L1CLPWEtOWxALWk8kj08bNKMIFskCGiRuJEGdNgZGx5+CTYzyd62dB6JM88KDvbi0cI/I/mZNO8OCXs2CeZnEj/brOX425M3PviJRwsYMDYg2Dwg4gABDahaRsEoGAWjYBRgAABP80txHDY2xwAAAABJRU5ErkJggg==","orcid":"","institution":"Henan University","correspondingAuthor":true,"prefix":"","firstName":"Huaping","middleName":"","lastName":"CHEN","suffix":""}],"badges":[],"createdAt":"2026-03-08 12:23:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9064129/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9064129/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105034069,"identity":"37caf9e9-4284-4bb2-86b3-725a8e299f79","added_by":"auto","created_at":"2026-03-20 07:22:35","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1103599,"visible":true,"origin":"","legend":"","description":"","filename":"PMEAR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9064129/v1_covered_56347d48-0d28-4785-8802-c5da9ad1a26f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Parsimonious and Efficient Integer-valued Autoregressive Process: Inference and Application","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Integer-valued time series, overdispersion, mixed Poisson distribution family, autoregressive process, CML estimation, asymptotic property","lastPublishedDoi":"10.21203/rs.3.rs-9064129/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9064129/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Negative Binomial AutoRegressive-type (NBAR) processes serve as a primary methodological frameworkfor the overdispersed integer-valued time series.However, the factorial terms and the turning parameter inherenting in the probability mass functionrender the model's likelihood function structurally intricate, thereby incurring substantial computational costs.To mitigate this dilemma, a new parsimonious yet efficient integer-valued autoregressive process is proposed,which is specifically built upon the Poisson moment exponential (PME) distribution.As a member of the mixed Poisson family,the PME distribution not only exhibits a more parsimonious structure, but alsoovercomes overdispersionwithout resorting to factorial terms or extra parameters. 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