Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey

Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey | 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 Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey Apollinaire BATOURE BAMANA, Yannick SOKDOU BILA LAMOU, David Jaures FOTSA-MBOGNE, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6289779/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 Stationarity in time series is a key property for practical data analysis, inferences, and predictions particularly in biosciences. Stationarity can be either deterministic or stochastic. If a time series data is not stationary, it can be rendered stationary through detrending or differentiation techniques. Differentiation can be performed in either an integer or fractional form. This paper investigates non-stationarity in time series data, focusing specifically on stochastic trends characterised by a unit root. It hypothesises that fractional differentiation can enhance forecast accuracy for datasets with limited volume. For experiments, 24 series corresponding to weekly Malaria and Typhoid Fever from Adamawa Region (Cameroon) are analysed and forecasted. Each series comprises 156 observations covering January 2021 to December 2023. After collecting, checking and classifying the data, four forecasting models, Auto Regressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Long Short-Term Memory (LSTM), and the proposed Fractional Differencing and LSTM (FD-LSTM), are implemented. The models' performances are evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of determination (R²) metrics, which inform further analysis and recommendations. Results reveal that ARFIMA outperformed the ARIMA by 93% in training and 100% in testing. Similarly, FD-LSTM achieved a 100% improvement over LSTM in training and testing. These findings underscore the value of achieving stationarity through fractional differentiation, enhancing model performance and providing a robust framework for forecasting in datasets with limited observations. Biostatistics Bioinformatics Artificial Intelligence and Machine Learning Health time series Limited time series data Non-stationarity Stochastic trend Classical differentiation Fractional differentiation. Full Text Additional Declarations The authors declare no competing interests. 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-6289779","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":432768298,"identity":"ba2880c7-3a14-45f8-85c5-e217c388f47d","order_by":0,"name":"Apollinaire BATOURE 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Stationarity can be either deterministic or stochastic. If a time series data is not stationary, it can be rendered stationary through detrending or differentiation techniques. Differentiation can be performed in either an integer or fractional form. This paper investigates non-stationarity in time series data, focusing specifically on stochastic trends characterised by a unit root. It hypothesises that fractional differentiation can enhance forecast accuracy for datasets with limited volume. For experiments, 24 series corresponding to weekly Malaria and Typhoid Fever from Adamawa Region (Cameroon) are analysed and forecasted. Each series comprises 156 observations covering January 2021 to December 2023. After collecting, checking and classifying the data, four forecasting models, Auto Regressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Long Short-Term Memory (LSTM), and the proposed Fractional Differencing and LSTM (FD-LSTM), are implemented. The models' performances are evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of determination (R\u0026sup2;) metrics, which inform further analysis and recommendations. Results reveal that ARFIMA outperformed the ARIMA by 93% in training and 100% in testing. Similarly, FD-LSTM achieved a 100% improvement over LSTM in training and testing. These findings underscore the value of achieving stationarity through fractional differentiation, enhancing model performance and providing a robust framework for forecasting in datasets with limited observations.\u003c/p\u003e","manuscriptTitle":"Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-25 04:37:33","doi":"10.21203/rs.3.rs-6289779/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":"64961f88-92e0-48c0-a422-8e5529e1c6c0","owner":[],"postedDate":"March 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":46086720,"name":"Biostatistics"},{"id":46086721,"name":"Bioinformatics"},{"id":46086722,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-03-25T04:37:33+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-25 04:37:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6289779","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6289779","identity":"rs-6289779","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}