Lag-Length Hyperparameter Impacts on Unit Root Testing: Toward Robust SARIMA Integration Order Estimation

Lag-Length Hyperparameter Impacts on Unit Root Testing: Toward Robust SARIMA Integration Order Estimation | 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 Lag-Length Hyperparameter Impacts on Unit Root Testing: Toward Robust SARIMA Integration Order Estimation Mohamed Slimane, Neila Bedioui, Mongi Besbes This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7656296/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Dec, 2025 Read the published version in International Journal of Data Science and Analytics → Version 1 posted 13 You are reading this latest preprint version Abstract Accurate estimation of integration orders (d,D) is a foundational step in SARIMA modeling, directly influencing model stationarity, predictive performance, and structural stability. However, the sensitivity of these estimates to lag-length hyperparameterization within unit root testing procedures remains underexplored. This study investigates the computational impact of various lag-selection strategies—specifically AIC, BIC, HQIC, t-statistics, and rule-based heuristics—on the determination of differencing orders in the context of natural gas demand forecasting. Using high-resolution hourly consumption data from ten Gas Pressure Reducing and Metering Stations (GPRMS) in Central Tunisia (2015–2023), we conduct extensive simulations across multiple temporal aggregations (weekly, monthly, quarterly). Integration orders were derived using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests, applied under varying lag-length configurations. The resulting SARIMA models were benchmarked using MAPE and the Overall Weighted Average (OWA) metrics. Results reveal significant variation in model performance tied to lag-length selection, particularly for low-frequency data, where BIC-based selection consistently achieved superior accuracy and stability. In contrast, t-stat heuristics led to over-differencing in some high-frequency cases. These findings highlight the critical role of lag-length specification in statistical preprocessing and provide practical recommendations for enhancing robustness in time series modeling workflows. Natural gas demand SARIMA Unit Root Testing Integration orders Lag length Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 04 Dec, 2025 Read the published version in International Journal of Data Science and Analytics → Version 1 posted Editorial decision: Revision requested 31 Oct, 2025 Reviews received at journal 31 Oct, 2025 Reviews received at journal 20 Oct, 2025 Reviewers agreed at journal 16 Oct, 2025 Reviewers agreed at journal 15 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers invited by journal 14 Oct, 2025 Editor assigned by journal 13 Oct, 2025 Submission checks completed at journal 20 Sep, 2025 First submitted to journal 19 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-7656296","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":534274835,"identity":"240ee6eb-7cd8-4bb1-b7ee-3542a1f802ac","order_by":0,"name":"Mohamed 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Estimation","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":"international-journal-of-data-science-and-analytics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jdsa","sideBox":"Learn more about [International Journal of Data Science and Analytics](http://link.springer.com/journal/41060)","snPcode":"41060","submissionUrl":"https://submission.nature.com/new-submission/41060/3","title":"International Journal of Data Science and Analytics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Natural gas demand, SARIMA, Unit Root Testing, Integration orders, Lag length","lastPublishedDoi":"10.21203/rs.3.rs-7656296/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7656296/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate estimation of integration orders (d,D) is a foundational step in SARIMA modeling, directly influencing model stationarity, predictive performance, and structural stability. However, the sensitivity of these estimates to lag-length hyperparameterization within unit root testing procedures remains underexplored. This study investigates the computational impact of various lag-selection strategies\u0026mdash;specifically AIC, BIC, HQIC, t-statistics, and rule-based heuristics\u0026mdash;on the determination of differencing orders in the context of natural gas demand forecasting. Using high-resolution hourly consumption data from ten Gas Pressure Reducing and Metering Stations (GPRMS) in Central Tunisia (2015\u0026ndash;2023), we conduct extensive simulations across multiple temporal aggregations (weekly, monthly, quarterly). Integration orders were derived using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests, applied under varying lag-length configurations. The resulting SARIMA models were benchmarked using MAPE and the Overall Weighted Average (OWA) metrics. Results reveal significant variation in model performance tied to lag-length selection, particularly for low-frequency data, where BIC-based selection consistently achieved superior accuracy and stability. In contrast, t-stat heuristics led to over-differencing in some high-frequency cases. These findings highlight the critical role of lag-length specification in statistical preprocessing and provide practical recommendations for enhancing robustness in time series modeling workflows.\u003c/p\u003e","manuscriptTitle":"Lag-Length Hyperparameter Impacts on Unit Root Testing: Toward Robust SARIMA Integration Order Estimation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-28 15:57:49","doi":"10.21203/rs.3.rs-7656296/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-31T09:49:54+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-31T08:54:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-20T11:06:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"317199911350440198330816751833920982969","date":"2025-10-16T07:30:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"293608995718549701629373190202561560106","date":"2025-10-15T14:02:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18122951344863915306459564962566305214","date":"2025-10-14T09:57:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"105454385708511168483291962147500227057","date":"2025-10-14T08:00:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"267925499429896916164938230149174954957","date":"2025-10-14T05:05:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"83020163648463928542763503757054083469","date":"2025-10-14T04:58:50+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-14T04:52:52+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-14T02:32:15+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-20T05:31:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Data Science and Analytics","date":"2025-09-19T08:28:19+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-data-science-and-analytics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jdsa","sideBox":"Learn more about [International Journal of Data Science and Analytics](http://link.springer.com/journal/41060)","snPcode":"41060","submissionUrl":"https://submission.nature.com/new-submission/41060/3","title":"International Journal of Data Science and Analytics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5895e98d-ebae-4da1-ba0c-30f501967422","owner":[],"postedDate":"October 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-08T16:07:22+00:00","versionOfRecord":{"articleIdentity":"rs-7656296","link":"https://doi.org/10.1007/s41060-025-00978-7","journal":{"identity":"international-journal-of-data-science-and-analytics","isVorOnly":false,"title":"International Journal of Data Science and Analytics"},"publishedOn":"2025-12-04 15:57:21","publishedOnDateReadable":"December 4th, 2025"},"versionCreatedAt":"2025-10-28 15:57:49","video":"","vorDoi":"10.1007/s41060-025-00978-7","vorDoiUrl":"https://doi.org/10.1007/s41060-025-00978-7","workflowStages":[]},"version":"v1","identity":"rs-7656296","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7656296","identity":"rs-7656296","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}