Periodicity Makes Perfect : Using Fourier Inspired Periodicity to Improve Long Horizon Time Series Forecasting

Periodicity Makes Perfect : Using Fourier Inspired Periodicity to Improve Long Horizon Time Series Forecasting | 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 Periodicity Makes Perfect : Using Fourier Inspired Periodicity to Improve Long Horizon Time Series Forecasting Tayyab Saeed Qureshi, Asma Ahmad Farhan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7764703/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Mar, 2026 Read the published version in Signal, Image and Video Processing → Version 1 posted 9 You are reading this latest preprint version Abstract Long-horizon Time Series Forecasting (LTSF) is a critical area of research that allows us to plan for the long term goals specially in energy, finance, healthcare, and climate science sectors. Transformers, and their derivatives form the leading edge of Artificial Intelligence (AI) research in almost all domains. However, in LTSF, resource heavy transformer based models and light weight linear models have performed similarly across the benchmark datasets. One critical difference between time series data and other data fields is the periodicity. Thus, performance of LTSF models can be enhanced by focusing on periodicity of data. However, many famous time series models do not prioritize periodicity, during their calculations. In this study, we improve performance of three foundational time series models including 2 linear (NLinear and DLinear) as well as one based on transformer backbone (iTransformer). We evaluate the performance of models across five benchmark datasets including ECL, ETT h1 \& h2, Traffic and Weather. We demonstrate an average improvement of 3.86% and 9.51% over our base models (iTransformer and NLinear / DLinear respectively) which demonstrates that simply adding periodicity in time series models can improve performance of formative models and bring them at par with the State-Of-The-Art (SOTA) models. Time Series Long-Horizon Time Series Forecasting LTSF Fourier Analysis Networks Time Series Prediction Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Mar, 2026 Read the published version in Signal, Image and Video Processing → Version 1 posted Reviewers agreed at journal 11 Nov, 2025 Reviewers agreed at journal 31 Oct, 2025 Reviews received at journal 26 Oct, 2025 Reviewers agreed at journal 20 Oct, 2025 Reviewers agreed at journal 19 Oct, 2025 Reviewers invited by journal 19 Oct, 2025 Editor assigned by journal 03 Oct, 2025 Submission checks completed at journal 03 Oct, 2025 First submitted to journal 02 Oct, 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. 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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-7764703","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":548298440,"identity":"3553e50d-74a4-4370-b8ea-401517fa9c26","order_by":0,"name":"Tayyab Saeed Qureshi","email":"","orcid":"","institution":"National University of Computer and Emerging Sciences","correspondingAuthor":false,"prefix":"","firstName":"Tayyab","middleName":"Saeed","lastName":"Qureshi","suffix":""},{"id":548298441,"identity":"c44af527-948e-43ba-a824-11117d2e676f","order_by":1,"name":"Asma Ahmad 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Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Time Series, Long-Horizon Time Series Forecasting, LTSF, Fourier Analysis Networks, Time Series Prediction","lastPublishedDoi":"10.21203/rs.3.rs-7764703/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7764703/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLong-horizon Time Series Forecasting (LTSF) is a critical area of research that allows us to plan for the long term goals specially in energy, finance, healthcare, and climate science sectors. Transformers, and their derivatives form the leading edge of Artificial Intelligence (AI) research in almost all domains. However, in LTSF, resource heavy transformer based models and light weight linear models have performed similarly across the benchmark datasets. One critical difference between time series data and other data fields is the periodicity. Thus, performance of LTSF models can be enhanced by focusing on periodicity of data. However, many famous time series models do not prioritize periodicity, during their calculations. In this study, we improve performance of three foundational time series models including 2 linear (NLinear and DLinear) as well as one based on transformer backbone (iTransformer). We evaluate the performance of models across five benchmark datasets including ECL, ETT h1 \\\u0026amp; h2, Traffic and Weather. We demonstrate an average improvement of 3.86% and 9.51% over our base models (iTransformer and NLinear / DLinear respectively) which demonstrates that simply adding periodicity in time series models can improve performance of formative models and bring them at par with the State-Of-The-Art (SOTA) models.\u003c/p\u003e","manuscriptTitle":"Periodicity Makes Perfect : Using Fourier Inspired Periodicity to Improve Long Horizon Time Series Forecasting","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-25 08:05:03","doi":"10.21203/rs.3.rs-7764703/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"328558699955835009992151678484321228797","date":"2025-11-11T07:38:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326107641892779239556664081037377275929","date":"2025-10-31T19:34:39+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-26T17:59:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"13218243047906364797458940896877085597","date":"2025-10-20T18:09:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"241664753543969164461461460229784628317","date":"2025-10-19T16:53:42+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-19T16:31:23+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-04T02:48:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-04T02:48:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Signal, Image and Video Processing","date":"2025-10-02T07:56:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"signal-image-and-video-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sivp","sideBox":"Learn more about [Signal, Image and Video Processing](http://link.springer.com/journal/11760)","snPcode":"11760","submissionUrl":"https://submission.nature.com/new-submission/11760/3","title":"Signal, Image and Video Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c96314f1-92f6-41e8-ba66-1c06c2405e00","owner":[],"postedDate":"November 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-09T16:08:33+00:00","versionOfRecord":{"articleIdentity":"rs-7764703","link":"https://doi.org/10.1007/s11760-026-05223-7","journal":{"identity":"signal-image-and-video-processing","isVorOnly":false,"title":"Signal, Image and Video Processing"},"publishedOn":"2026-03-06 15:59:56","publishedOnDateReadable":"March 6th, 2026"},"versionCreatedAt":"2025-11-25 08:05:03","video":"","vorDoi":"10.1007/s11760-026-05223-7","vorDoiUrl":"https://doi.org/10.1007/s11760-026-05223-7","workflowStages":[]},"version":"v1","identity":"rs-7764703","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7764703","identity":"rs-7764703","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}