Air Passengers Time Series Forecasting using ARIMA

Air Passengers Time Series Forecasting using ARIMA | 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PDF Research Article Air Passengers Time Series Forecasting using ARIMA Manish Shukla This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7419928/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 The number of people who fly on commercial aircraft has grown markedly since the middle of the twentieth century. Reliable forecasts of air passenger demand help airlines and regulators plan fleets, schedules and infrastructure. The AirPassengers data set — monthly counts of international airline passengers from 1949 to 1960 — is a classic benchmark for time series analysis because it exhibits both trend and seasonality [2]. In this report I revisit these data from a practical point of view. Inspired by a publicly available repository of code and plots8, I outline a reproducible workflow that involves exploratory graphics, variance-stabilising transformations, stationarity testing, decomposition of trend and seasonality, autocorrelation analysis and the fitting of a seasonal ARIMA model. I split the series into training and test samples, compare competing models using information criteria, and evaluate out-of-sample forecasts using root mean square error and mean absolute percentage error. The emphasis throughout is on clarity and brevity rather than exhaustiveness. The accompanying scripts and figures make it straightforward for readers to replicate the analysis and adapt the approach to other seasonal time series. 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. 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-7419928","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":503272165,"identity":"a3b9b9dc-0569-4d7f-b938-a696cd859e24","order_by":0,"name":"Manish Shukla","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Manish","middleName":"","lastName":"Shukla","suffix":""}],"badges":[],"createdAt":"2025-08-20 18:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7419928/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7419928/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89618166,"identity":"9f95d637-40e7-4a4e-91bf-d85b8164f259","added_by":"auto","created_at":"2025-08-22 03:38:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":467957,"visible":true,"origin":"","legend":"","description":"","filename":"AirPassengers.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7419928/v1_covered_3beccdcc-7927-48fc-90ea-b46260bd41f1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Air Passengers Time Series Forecasting using ARIMA","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-7419928/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7419928/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The number of people who fly on commercial aircraft has grown markedly since the middle\nof the twentieth century. Reliable forecasts of air passenger demand help airlines and regulators\nplan fleets, schedules and infrastructure. The AirPassengers data set — monthly counts\nof international airline passengers from 1949 to 1960 — is a classic benchmark for time series\nanalysis because it exhibits both trend and seasonality [2]. In this report I revisit these data\nfrom a practical point of view. Inspired by a publicly available repository of code and plots8, I\noutline a reproducible workflow that involves exploratory graphics, variance-stabilising transformations,\nstationarity testing, decomposition of trend and seasonality, autocorrelation analysis\nand the fitting of a seasonal ARIMA model. I split the series into training and test samples,\ncompare competing models using information criteria, and evaluate out-of-sample forecasts using\nroot mean square error and mean absolute percentage error. The emphasis throughout is\non clarity and brevity rather than exhaustiveness. The accompanying scripts and figures make\nit straightforward for readers to replicate the analysis and adapt the approach to other seasonal\ntime series.","manuscriptTitle":"Air Passengers Time Series Forecasting using ARIMA","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-22 03:30:01","doi":"10.21203/rs.3.rs-7419928/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":"c92a1b4f-b271-46ce-bad1-0da7e17b67f2","owner":[],"postedDate":"August 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-24T12:53:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-22 03:30:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7419928","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7419928","identity":"rs-7419928","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}