Auxiliary-lag Dependent Gaussian Process Model for Forecasting Using Proposed Kernels and Multi-start Optimization Method

Auxiliary-lag Dependent Gaussian Process Model for Forecasting Using Proposed Kernels and Multi-start Optimization Method | 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 Auxiliary-lag Dependent Gaussian Process Model for Forecasting Using Proposed Kernels and Multi-start Optimization Method Haris Khurram This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6888051/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 Pakistan is currently affected by climate change and facing floods due to monsoon rains. Also, it impacts agriculture production, and being an agricultural land, it has a significant role in the economy of Pakistan. Rainfall and agriculture production forecasting are very important for policy making. In this paper, we have presented an auxiliary-lag dependent Gaussian process, a Bayesian non-parametric machine learning model, for forecasting using auxiliary lags. We have also introduced some new multifeatured kernel functions that are versatile in dealing with seasonal data. For comparison of the proposed model, we have used the autoregressive random forest model, autoregressive artificial neural network model, seasonal autoregressive moving average models, and exponential smoothing models. Results confirmed the superiority of the proposed model over conventional models. The proposed methodology will be helpful for other researchers and local experts in making more reliable forecasting which will be helpful in policymaking relevant to agriculture systems, water management systems, climate change, and natural disasters such as droughts and floods. Gaussian Process Machine learning models Auxiliary Lags Kernel functions Forecasting Rainfall Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterialS1.docx 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. 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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-6888051","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486819283,"identity":"47ff9b9b-2378-474e-875e-ba42d928a1e6","order_by":0,"name":"Haris Khurram","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYBACAyA+wMCQkADhVsAFE4jVcoZILQxwLYxtRGgxZz/78OAPhrQ8g9tnH366Oe9OYgN78zYJxh1pOLVY9qQbHOZhyCk2OJduLJ277VliA8+xMgnGMzm4HXYgjeEw0NuJG86wMQC1HE5skMgxk2Bsq8Ct5fwzBqDDwFqYf+fOAWqRf0NAy400hgNAh4G0sEnnNoBs4QFpweOwG88YDvMYpCXOBGqxzjl22LiNJ63YIvEMbu8bnE9j/vijIjmxD+iw2zk1h2X72Q9vvPFxRzJOLVCNSGw2EJHYQEAHJmAkXcsoGAWjYBQMXwAA82xXdd8tLL8AAAAASUVORK5CYII=","orcid":"","institution":"National University of Computer and Emerging Sciences","correspondingAuthor":true,"prefix":"","firstName":"Haris","middleName":"","lastName":"Khurram","suffix":""}],"badges":[],"createdAt":"2025-06-13 12:08:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6888051/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6888051/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100787562,"identity":"cf1d6320-a62e-4fb7-980b-07742b620d1f","added_by":"auto","created_at":"2026-01-21 12:02:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1040871,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6888051/v1_covered_b8f6d5c7-420c-49e8-9353-8e084de34843.pdf"},{"id":87181214,"identity":"e00d7e2b-cd90-46ad-a8fd-5f6d5bc94d5d","added_by":"auto","created_at":"2025-07-21 09:47:12","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1848171,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterialS1.docx","url":"https://assets-eu.researchsquare.com/files/rs-6888051/v1/599c476c8e5119109e09cd95.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Auxiliary-lag Dependent Gaussian Process Model for Forecasting Using Proposed Kernels and Multi-start Optimization Method","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":"Gaussian Process, Machine learning models, Auxiliary Lags, Kernel functions, Forecasting, Rainfall","lastPublishedDoi":"10.21203/rs.3.rs-6888051/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6888051/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePakistan is currently affected by climate change and facing floods due to monsoon rains. 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