Multi-output Ensembles for Multi-step Forecasting

Multi-output Ensembles for Multi-step Forecasting | 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Article Multi-output Ensembles for Multi-step Forecasting Vitor Cerqueira, Luis Torgo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3119564/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper studies the application of ensembles composed of multi-output models for multi-step ahead forecasting problems. Dynamic ensembles have been commonly used for forecasting. However, these are typically designed for one-step ahead tasks. On the other hand, the literature regarding the application of dynamic ensembles for multi-step aheadforecasting is scarce. Moreover, it is not clear how the combination rule is applied across the forecasting horizon. We carried out extensive experiments to analyze the application of dynamic ensembles for multi-step forecasting. We resorted to a case study with 3568 time series and an ensemble of 30 multi-output models. We discovered that dynamic ensembles based on arbitrating and windowing present the best performance according to average rank. Moreover, as the horizon increases, most approaches struggle to outperform a static ensemble that assigns equal weights to all models. The experiments are publicly available in a repository. Ensemble methods Time series forecasting Multi-output models Time series Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-3119564","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":214218977,"identity":"a399e3a2-310b-4308-b8bb-8dcbaf6999fd","order_by":0,"name":"Vitor Cerqueira","email":"data:image/png;base64,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","orcid":"","institution":"Dalhousie University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Vitor","middleName":"","lastName":"Cerqueira","suffix":""},{"id":214218978,"identity":"ef049149-5c0f-48c3-b6ac-06eb3327189c","order_by":1,"name":"Luis Torgo","email":"","orcid":"","institution":"Dalhousie University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Luis","middleName":"","lastName":"Torgo","suffix":""}],"badges":[],"createdAt":"2023-06-28 09:29:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3119564/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3119564/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":56307332,"identity":"5a273047-e2c3-47f5-a788-6ee7bd2b2637","added_by":"auto","created_at":"2024-05-11 13:09:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":294077,"visible":true,"origin":"","legend":"","description":"","filename":"sub.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3119564/v1_covered_b5a3fc98-bdbd-4260-8cf2-81c07454f382.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Multi-output Ensembles for Multi-step Forecasting","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Ensemble methods, Time series forecasting, Multi-output models, Time series","lastPublishedDoi":"10.21203/rs.3.rs-3119564/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3119564/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper studies the application of ensembles composed of multi-output models for multi-step ahead forecasting problems. 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