CP-LLM: Conformal Calibration for Time Series Interval Forecasting with Frozen Large Language Model

CP-LLM: Conformal Calibration for Time Series Interval Forecasting with Frozen Large Language Model | 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 CP-LLM: Conformal Calibration for Time Series Interval Forecasting with Frozen Large Language Model Ke Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9291769/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 Reliable prediction intervals are essential for deploying time-series forecasting systems in high-stakes domains, yet uncertainty estimates from frozen large language models (LLMs) often deviate from nominal confidence levels. This paper studies interval calibration for multi-step forecasting with frozen LLMs and proposes CP-LLM, a fine-tuning-free two-stage post-hoc framework. In Stage 1, base intervals are constructed from sampled LLM forecasts and augmented with three complementary uncertainty signals: sampling dispersion, temperature sensitivity, and serialization perturbation sensitivity. In Stage 2, base intervals are calibrated on a held-out calibration segment using either Conformalized Quantile Regression (CQR) for relatively stable regimes or Adaptive Conformal Inference (ACI) under temporal distribution shift. Experiments on five public univariate datasets with four API-accessed frozen LLMs show that CP-LLM substantially reduces coverage bias while maintaining competitive interval sharpness. Additional comparisons with traditional forecasting methods, together with ablation and parameter-sensitivity analyses, provide further evidence for the effectiveness of the proposed framework. Time series forecasting Prediction intervals Large language models Conformal prediction Uncertainty quantification Full Text Additional Declarations The authors declare no competing interests. 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-9291769","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615928465,"identity":"4e6c39f3-8575-4748-87c9-f1e2df8edf19","order_by":0,"name":"Ke Li","email":"data:image/png;base64,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","orcid":"","institution":"Nanjing Auditing University","correspondingAuthor":true,"prefix":"","firstName":"Ke","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2026-04-01 12:21:01","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9291769/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9291769/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106093539,"identity":"f3a64f2a-7d29-4f0a-86c5-c3732617cbde","added_by":"auto","created_at":"2026-04-03 11:37:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1037996,"visible":true,"origin":"","legend":"","description":"","filename":"SpringerLectureNotesinComputerScience22.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9291769/v1_covered_5ca6bfe6-c522-43fd-bc5f-9ed44db9fed2.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eCP-LLM: Conformal Calibration for Time Series Interval Forecasting with Frozen Large Language Model\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Time series forecasting, Prediction intervals, Large language models, Conformal prediction, Uncertainty quantification","lastPublishedDoi":"10.21203/rs.3.rs-9291769/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9291769/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eReliable prediction intervals are essential for deploying time-series forecasting systems in high-stakes domains, yet uncertainty estimates from frozen large language models (LLMs) often deviate from nominal confidence levels. 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