{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T08:47:00Z","timestamp":1791794820488,"version":"4.3.4"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>This paper develops a mathematically rigorous framework for probabilistic market inference that operates on residuals-the idiosyncratic price movements remaining after dynamic removal of macroeconomic factors via robust Kalman filteringrather than on raw equity returns. The framework integrates five established methodological components into a unified pipeline: (i) state-space models with Student-t robust extensions for time-varying hedge coefficient estimation; (ii) a triple-validation causality gauntlet combining cross-correlation, Granger causality, and transfer entropy for nonlinear lead-lag detection; (iii) a recursive Bayesian confidence cascade of depth N , where N scales with the number of heterogeneous signal sources, computing the posterior probability that each probability estimate is wellcalibrated; (iv) Markov-switching regime detection augmented by Hurst exponent monitoring for autocorrelation structure shifts; and (v) fractional Kelly criterion position sizing derived from information-theoretic growth rate bounds, with effective probability inputs from the full Bayesian cascade. Applied to Brazilian equities (PETR4, BRFS3) using data fused from ten heterogeneous API sources-including macroeconomic indicators, commodity prices,&amp;nbsp;news sentiment, weather anomalies, and social media tone\u2014the framework reveals economically plausible lead\u2013lag relationships invisible to standard models: VALE3 residuals lead PETR4 by +2 days (p = 0.02), corn price residuals lead BRFS3 by +3 days (p = 0.01), and Paran\u00e1 rainfall anomalies lead BRFS3 by +7 days (p = 0.05). Critically, Reddit sentiment is shown to be synchronous and nonpredictive (p &amp;gt; 0.10), validating the framework\u2019s capacity to reject false signals. The architecture is designed not for human discretionary trading but as a theoretical foundation for autonomous AI inference engines that must quantify, propagate, and act upon nested uncertainty. The recursive cascade structure ensures that as the variable universe expands, the system\u2019s epistemic humility scales proportionally\u2014more information sources produce more uncertainty layers, naturally regularizing position sizes and preventing overconfident capital allocation.<\/jats:p>","DOI":"10.2139\/ssrn.7594458","type":"posted-content","created":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T08:20:26Z","timestamp":1791793226000},"source":"Crossref","is-referenced-by-count":0,"title":["From Residuals to Returns - A quantitative Approach to Capital Market with use of AI"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9201-3921","authenticated-orcid":true,"given":"Marcus","family":"Bergo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T08:20:26Z","timestamp":1791793226000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7594458"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7594458","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}