A quantum-like tensor state model for bivariate time series in forestry and residential construction

A quantum-like tensor state model for bivariate time series in forestry and residential construction | 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 A quantum-like tensor state model for bivariate time series in forestry and residential construction Jan Kotlarz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8852860/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 A quantum–inspired tensor state model for bivariate time series in business and industry is proposed and evaluated against a rich set of residual–based benchmark specifications. The model represents two related processes as a joint tensor product state in a four–dimensional complex Hilbert space and evolves this state via a parametrised unitary operator, which acts as a nonlinear second–stage correction on top of global linear forecasts. In an empirical application to timber harvesting and residential construction across 16 Polish voivodeships over 2005–2025, the tensor model is found to reduce the global mean squared error for harvesting amplitudes from 0.00112 for a pooled OLS baseline and 0.00095 for the best nonlinear tree benchmark to 0.00067, and to lower mean absolute error from 0.0227 and 0.0213 to 0.0177; for construction, MSE is reduced from 0.00223 (OLS) and 0.00157 (tree) to 0.00144, with MAE moving from 0.0366 and 0.0294 to 0.0308. Across regions, the tensor specification attains the lowest average harvesting error in about 90R y R y rotations of approximately 0.78 and 1.63 radians correspond to slow and fast adjustment scales of roughly eight and four years in the residual dynamics, and an entangling angle near 0.62 radians implies a substantial but not extreme two–way interaction between sectors. At the level of basis configurations, the fitted operator maps joint low and joint high residual states into each other with probability slightly above one half, while mixed states tend to remain mixed, suggesting that simultaneous booms or slumps in both sectors are relatively transient whereas cross–sector imbalances are more persistent. Together, these quantitative results indicate that quantum–like tensor models can deliver forecast accuracy that is at least competitive with strong classical benchmarks and, at the same time, provide a compact and business–interpretable summary of time–varying cross–sector dependence that is useful for planning and risk assessment. stochastic modelling quantum-inspired models tensor state bivariate time series forestry residential construction 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. 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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-8852860","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627530402,"identity":"06e2cde3-cae1-44d9-bf7e-e62a6bfc93f8","order_by":0,"name":"Jan Kotlarz","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYBACxgYIlgGxHzAwJDAwsBOnxYAHyGY2AGthJs4msBY2CaK0MLefPcA4o+IPD//s48+qeXPSGMwJaWHsyUtg3HDGgEfiXELabd5tOQyWzQQdlWPA+LAN6LAzDMeAWioYDA4T0tL/BqJF/gxjWzFxWmYAbdkI1GJwhpmNGeQwIrS8MTg444wxj+EZNmbJudvSeAj6xbA/x/BhT4WcnNwZ9ocf3m5LljNnbyCgBSh/AFmAx4CAJQzyGCIEtYyCUTAKRsGIAwDL1jyD1NZH0gAAAABJRU5ErkJggg==","orcid":"","institution":"Nicolaus Copernicus University","correspondingAuthor":true,"prefix":"","firstName":"Jan","middleName":"","lastName":"Kotlarz","suffix":""}],"badges":[],"createdAt":"2026-02-11 14:38:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8852860/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8852860/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107707123,"identity":"4476b04c-c353-4943-b9a4-12f004e6fbbc","added_by":"auto","created_at":"2026-04-24 09:19:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":785696,"visible":true,"origin":"","legend":"","description":"","filename":"paperlatex2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8852860/v1_covered_38d0ad99-3486-4bf0-958e-d4af4aa402f8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A quantum-like tensor state model for bivariate time series in forestry and residential construction","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":"stochastic modelling, quantum-inspired models, tensor state, bivariate time series, forestry, residential construction","lastPublishedDoi":"10.21203/rs.3.rs-8852860/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8852860/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA quantum–inspired tensor state model for bivariate time series in business and industry is proposed and evaluated against a rich set of residual–based benchmark specifications. The model represents two related processes as a joint tensor product state in a four–dimensional complex Hilbert space and evolves this state via a parametrised unitary operator, which acts as a nonlinear second–stage correction on top of global linear forecasts. In an empirical application to timber harvesting and residential construction across 16 Polish voivodeships over 2005–2025, the tensor model is found to reduce the global mean squared error for harvesting amplitudes from 0.00112 for a pooled OLS baseline and 0.00095 for the best nonlinear tree benchmark to 0.00067, and to lower mean absolute error from 0.0227 and 0.0213 to 0.0177; for construction, MSE is reduced from 0.00223 (OLS) and 0.00157 (tree) to 0.00144, with MAE moving from 0.0366 and 0.0294 to 0.0308. Across regions, the tensor specification attains the lowest average harvesting error in about 90R y R y rotations of approximately 0.78 and 1.63 radians correspond to slow and fast adjustment scales of roughly eight and four years in the residual dynamics, and an entangling angle near 0.62 radians implies a substantial but not extreme two–way interaction between sectors. At the level of basis configurations, the fitted operator maps joint low and joint high residual states into each other with probability slightly above one half, while mixed states tend to remain mixed, suggesting that simultaneous booms or slumps in both sectors are relatively transient whereas cross–sector imbalances are more persistent. Together, these quantitative results indicate that quantum–like tensor models can deliver forecast accuracy that is at least competitive with strong classical benchmarks and, at the same time, provide a compact and business–interpretable summary of time–varying cross–sector dependence that is useful for planning and risk assessment.\u003c/p\u003e","manuscriptTitle":"A quantum-like tensor state model for bivariate time series in forestry and residential construction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-24 06:11:47","doi":"10.21203/rs.3.rs-8852860/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"cd73ee29-c1f3-41a8-8d22-dfb9b1e9555e","owner":[],"postedDate":"April 24th, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"68775998388198607022079305477638259707","date":"2026-05-14T16:15:55+00:00","index":18,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-24T06:11:47+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-24 06:11:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8852860","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8852860","identity":"rs-8852860","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}