Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25

Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25 | 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 Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25 Varun Soman, Amaranathan Sabarinath This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7526100/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Understanding and predicting the shape and intensity of solar cycles is important for anticipating their effects on Earth. In this study, we present an interpretable analog-based forecasting framework. Using Dynamic Time Warping (DTW), we identify past solar cycles with similar morphology and blend them—after alignment in time and amplitude—to capture key features such as rise–decay asymmetry, cycle duration, and peak variation.To assess forecast uncertainty, we implement a phase-aware residual bootstrapping method based on historical prediction errors. This allows us to construct realistic, nonparametric confidence intervals. The framework is validated on Solar Cycles 20 to 24, showing strong performance in both peak amplitude and timing. All validation and figures are computed on a frozen SILSO monthly-smoothed dataset through 2024-12-01 (1749-07–2024-12; $N=3306$) under a fixed random seed to avoid look-ahead and ensure exact reproducibility. In this frozen setup, the $k=2$ configuration minimizes average RMSE across SC20–24 (Avg RMSE $=15.85$, $R^2 \approx 0.92$, $r \approx 0.97$).We then apply the method to forecast Solar Cycles 25 and 26 using only pre-cycle data, ensuring all projections remain within the bounds of historical variability. Baseline forecasts from the frozen snapshot yield SC25 peak $193.86$ at month $47$ (length $133$ months) and SC26 peak $151.66$ at month $42$ (length $129$ months). A real-time extension of the model updates analog selection as new SC25 observations become available. While this enhances short-term accuracy, it may introduce trade-offs in morphological coherence, particularly in capturing long-term shape features due to incomplete phase coverage. In the as-of-2024-12-01 real-time run, DTW selects SC17 and SC13 as analogs (weights $0.506$, $0.494$); on the observed SC25 window we obtain MAE $=11.15$, RMSE $=13.90$, $R^2=0.93$, $r=0.98$, with under-coverage of nominal 98% intervals ($\sim$47% zero-mean, $\sim$56% raw).Overall, the core model yields consistent and interpretable long-range forecasts, while the real-time variant offers greater adaptability at the expense of structural consistency. Solar cycle forecasting Sunspot number Dynamic Time Warp- ing Morphological similarity Forecast uncertainty Residual simulation Analog methods Real-time prediction Solar activity modeling Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 Oct, 2025 Reviews received at journal 06 Oct, 2025 Reviewers agreed at journal 11 Sep, 2025 Reviewers invited by journal 08 Sep, 2025 Editor assigned by journal 05 Sep, 2025 Submission checks completed at journal 05 Sep, 2025 First submitted to journal 03 Sep, 2025 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-7526100","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":513862308,"identity":"34a60d01-c004-482b-878a-8b1eb1132929","order_by":0,"name":"Varun Soman","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYDADfgYGNhDNDOVLENYi2UCyFoMDEC1EqDx+9pl0wZ9tecbXDj978HOPHTt//wHGDz8YLPJwajmTbiY9s+12sdntNHPDnmfJzBI3EpglexgkinF7IY1NmrfhduK22wlmEjwHmJkZbjAwSAP9ktiAS0v/MzZpnj+3EzfPTv8m+edAPbP8+QPMv/Fp4ZcA2sLDdjtxg3SOmTTPgcPMBgcS2PDawi/xjNmat+124ozbOWXSMgeOMxveSGyz7DHArYWNP43xNshh/bPTt0m+OVCdLHf+8OEbPyrqcGrBAMkMDIxAxQbEqgcCOxLUjoJRMApGwQgBAHGLUgl8lKlOAAAAAElFTkSuQmCC","orcid":"","institution":"Maharaja's College","correspondingAuthor":true,"prefix":"","firstName":"Varun","middleName":"","lastName":"Soman","suffix":""},{"id":513862309,"identity":"4b96b4f1-836b-42f0-b2ce-12a60c0c7aab","order_by":1,"name":"Amaranathan Sabarinath","email":"","orcid":"","institution":"Vikram Sarabhai Space Centre","correspondingAuthor":false,"prefix":"","firstName":"Amaranathan","middleName":"","lastName":"Sabarinath","suffix":""}],"badges":[],"createdAt":"2025-09-03 10:53:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7526100/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7526100/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91456622,"identity":"0b98fdd4-6372-4951-a914-cfacf787ae78","added_by":"auto","created_at":"2025-09-16 16:24:56","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":812748,"visible":true,"origin":"","legend":"","description":"","filename":"SpringerDTW.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7526100/v1_covered_0d55e889-9747-4077-a415-d11e23561016.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"solar-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sola","sideBox":"Learn more about [Solar Physics](http://link.springer.com/journal/11207)","snPcode":"11207","submissionUrl":"https://submission.nature.com/new-submission/11207/3","title":"Solar Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Solar cycle forecasting, Sunspot number, Dynamic Time Warp- ing, Morphological similarity, Forecast uncertainty, Residual simulation, Analog methods, Real-time prediction, Solar activity modeling","lastPublishedDoi":"10.21203/rs.3.rs-7526100/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7526100/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Understanding and predicting the shape and intensity of solar cycles is important for anticipating their effects on Earth. In this study, we present an interpretable analog-based forecasting framework. Using Dynamic Time Warping (DTW), we identify past solar cycles with similar morphology and blend them—after alignment in time and amplitude—to capture key features such as rise–decay asymmetry, cycle duration, and peak variation.To assess forecast uncertainty, we implement a phase-aware residual bootstrapping method based on historical prediction errors. This allows us to construct realistic, nonparametric confidence intervals. The framework is validated on Solar Cycles 20 to 24, showing strong performance in both peak amplitude and timing. All validation and figures are computed on a frozen SILSO monthly-smoothed dataset through 2024-12-01 (1749-07–2024-12; $N=3306$) under a fixed random seed to avoid look-ahead and ensure exact reproducibility. In this frozen setup, the $k=2$ configuration minimizes average RMSE across SC20–24 (Avg RMSE $=15.85$, $R^2 \\approx 0.92$, $r \\approx 0.97$).We then apply the method to forecast Solar Cycles 25 and 26 using only pre-cycle data, ensuring all projections remain within the bounds of historical variability. Baseline forecasts from the frozen snapshot yield SC25 peak $193.86$ at month $47$ (length $133$ months) and SC26 peak $151.66$ at month $42$ (length $129$ months). A real-time extension of the model updates analog selection as new SC25 observations become available. While this enhances short-term accuracy, it may introduce trade-offs in morphological coherence, particularly in capturing long-term shape features due to incomplete phase coverage. In the as-of-2024-12-01 real-time run, DTW selects SC17 and SC13 as analogs (weights $0.506$, $0.494$); on the observed SC25 window we obtain MAE $=11.15$, RMSE $=13.90$, $R^2=0.93$, $r=0.98$, with under-coverage of nominal 98\\% intervals ($\\sim$47\\% zero-mean, $\\sim$56\\% raw).Overall, the core model yields consistent and interpretable long-range forecasts, while the real-time variant offers greater adaptability at the expense of structural consistency.","manuscriptTitle":"Analog-Based Forecasting of Solar Cycles Using Dynamic Time Warping and Residual Bootstrapping: Real-Time Application to Cycle 25","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 16:16:48","doi":"10.21203/rs.3.rs-7526100/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-07T08:14:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-06T17:48:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"182811430471950507926144964927759520390","date":"2025-09-11T21:21:56+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-08T14:41:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-05T07:17:49+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-05T07:16:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"Solar Physics","date":"2025-09-03T10:38:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"solar-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sola","sideBox":"Learn more about [Solar Physics](http://link.springer.com/journal/11207)","snPcode":"11207","submissionUrl":"https://submission.nature.com/new-submission/11207/3","title":"Solar Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8d1be424-5ac9-4940-8fec-db653b4f0637","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-18T11:39:49+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-16 16:16:48","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7526100","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7526100","identity":"rs-7526100","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}