Recursive Standard Deviation Dynamics: Bridging Statistical Theory and Economic Applications through Iterative Feedback

Recursive Standard Deviation Dynamics: Bridging Statistical Theory and Economic Applications through Iterative Feedback | 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 Recursive Standard Deviation Dynamics: Bridging Statistical Theory and Economic Applications through Iterative Feedback Eyas Gaffar A. Osman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6184028/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 This study explores the dynamic behavior of standard deviation within a recursive feedback system, where the computed metric is iteratively appended to its dataset. Through extensive computational simulations, we demonstrate that standard deviation exhibits non-linear decay, asymptotically approaching a near-zero value while retaining a residual diversity floor (C ≈ 1.2×10⁻⁷). Initialized with a dataset [1, 2, ..., 10], the process reveals a two-phased decay: rapid initial decline (k ≈ 0.012) followed by gradual convergence. An exponential decay model, y(x) = 2.71e⁻⁰·⁰¹²ˣ + 1.2×10⁻⁷ (R² = 0.98), accurately captures this behavior, offering empirical insights into feedback-driven dynamics. These findings are contextualized within economic frameworks, including volatility modeling, adaptive policymaking, and machine learning-driven econometrics. The rapid decay mirrors financial market stabilization post-shock, while the diversity floor suggests inherent systemic risk, challenging complete risk elimination assumptions. For policymaking, the decay constant informs stabilization efficacy, and the asymptote sets realistic inflation volatility targets. In machine learning, preserving residual diversity enhances algorithmic robustness. This bridges statistical theory and economic practice, providing actionable insights for financial risk management, policy design, and trading strategies. Unlike traditional linear models (e.g., ARIMA), our recursive approach captures non-linear feedback effects, addressing a critical research gap. Future work should integrate stochastic elements for broader applicability. Recursive feedback standard deviation decay economic modeling volatility dynamic systems 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-6184028","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":447573807,"identity":"df012d56-1327-4165-9ece-12906506a1d8","order_by":0,"name":"Eyas Gaffar A. 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Through extensive computational simulations, we demonstrate that standard deviation exhibits non-linear decay, asymptotically approaching a near-zero value while retaining a residual diversity floor (C\u0026thinsp;\u0026asymp;\u0026thinsp;1.2\u0026times;10⁻⁷). Initialized with a dataset [1, 2, ..., 10], the process reveals a two-phased decay: rapid initial decline (k\u0026thinsp;\u0026asymp;\u0026thinsp;0.012) followed by gradual convergence. An exponential decay model, y(x)\u0026thinsp;=\u0026thinsp;2.71e⁻⁰\u0026middot;⁰\u0026sup1;\u0026sup2;ˣ + 1.2\u0026times;10⁻⁷ (R\u0026sup2; = 0.98), accurately captures this behavior, offering empirical insights into feedback-driven dynamics. These findings are contextualized within economic frameworks, including volatility modeling, adaptive policymaking, and machine learning-driven econometrics. The rapid decay mirrors financial market stabilization post-shock, while the diversity floor suggests inherent systemic risk, challenging complete risk elimination assumptions. For policymaking, the decay constant informs stabilization efficacy, and the asymptote sets realistic inflation volatility targets. In machine learning, preserving residual diversity enhances algorithmic robustness. This bridges statistical theory and economic practice, providing actionable insights for financial risk management, policy design, and trading strategies. Unlike traditional linear models (e.g., ARIMA), our recursive approach captures non-linear feedback effects, addressing a critical research gap. 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