TG-LLM: Temporal Graph as Enhanced Embedding for Time Series Forecasting with LLMs

TG-LLM: Temporal Graph as Enhanced Embedding for Time Series Forecasting with LLMs | 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 TG-LLM: Temporal Graph as Enhanced Embedding for Time Series Forecasting with LLMs Ke Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9513473/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 Large Language Models (LLMs) have demonstrated potential in time series forecasting, but their self-attention mechanism is inherently token-to-token and fails to capture temporal dependencies within each variable’s series or correlations across variables in multivariate settings, thus limiting forecasting accuracy. Moreover, time series are often non-stationary, with patterns that vary across temporal scales, making it difficult for models to separate multi-scale features. To address these limitations, we propose Temporal Graph with LLM (TG-LLM), an LLM-based framework that enriches the embedding stage with two complementary modules before feeding a frozen LLM. The Wavelet Decomposition module decomposes each variable’s series into frequency-level components (trend, high-frequency detail, and residual) to capture multi-scale temporal patterns and handle non-stationarity. The Temporal Graph module constructs a graph over time steps and variables, encodes it with a Graph Convolutional Network (GCN), and fuses the resulting structural embeddings with patch embeddings to explicitly represent temporal dependencies and cross-variable correlations. These enhanced embeddings are concatenated with task-specific prompts and fed into a frozen LLM for forecasting. Extensive experiments on long-term and short-term benchmarks demonstrate that TG-LLM achieves strong and consistent forecasting performance, outperforming existing LLM-based methods and competitive deep learning baselines. Ablation studies confirm that both modules contribute individually and synergistically to the overall performance gains. Theoretical Computer Science Time series forecasting Temporal graph Wavelet decomposition Large language model Graph convolutional network 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. 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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-9513473","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628779031,"identity":"a791d9df-8d82-483d-8ee9-2dd5f4188cb2","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":"2026-04-24 07:06:37","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9513473/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9513473/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108074166,"identity":"328c5493-76d9-4058-ab4a-a79619c96f4d","added_by":"auto","created_at":"2026-04-29 06:26:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1941350,"visible":true,"origin":"","legend":"","description":"","filename":"TGLLMTemporalGraphasEnhancedEmbeddingforTimeSeriesForecastingwithLLMs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9513473/v1_covered_a0fd52e0-9c19-4c61-869b-e92c5d62cceb.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eTG-LLM: Temporal Graph as Enhanced Embedding for Time Series Forecasting with LLMs\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Nanjing Audit University","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, Temporal graph, Wavelet decomposition, Large language model, Graph convolutional network","lastPublishedDoi":"10.21203/rs.3.rs-9513473/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9513473/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLarge Language Models (LLMs) have demonstrated potential in time series forecasting, but their self-attention mechanism is inherently token-to-token and fails to capture temporal dependencies within each variable’s series or correlations across variables in multivariate settings, thus limiting forecasting accuracy. Moreover, time series are often non-stationary, with patterns that vary across temporal scales, making it difficult for models to separate multi-scale features. To address these limitations, we propose Temporal Graph with LLM (TG-LLM), an LLM-based framework that enriches the embedding stage with two complementary modules before feeding a frozen LLM. The Wavelet Decomposition module decomposes each variable’s series into frequency-level components (trend, high-frequency detail, and residual) to capture multi-scale temporal patterns and handle non-stationarity. The Temporal Graph module constructs a graph over time steps and variables, encodes it with a Graph Convolutional Network (GCN), and fuses the resulting structural embeddings with patch embeddings to explicitly represent temporal dependencies and cross-variable correlations. These enhanced embeddings are concatenated with task-specific prompts and fed into a frozen LLM for forecasting. 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