{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T20:00:00Z","timestamp":1791489600858,"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":"<div>\n This paper introduces a geometric framework that decomposes the quality of time-series\n<\/div>\n<div>\n momentum signals through the lens of information geometry. We embed the distribu-\n<\/div>\n<div>\n tional dynamics of each asset into a statistical manifold endowed with the Fisher-Rao\n<\/div>\n<div>\n metric, and extract a coordinate-free diagnostic-directional purity (\u03a6), that isolates the\n<\/div>\n<div>\n fraction of distributional movement attributable to location shifts rather than scale dis-\n<\/div>\n<div>\n tortions. We show that weighting momentum positions by \u03a6\u03b1 (\u03b1 &gt; 0) yields a strat-\n<\/div>\n<div>\n egy we call Information-Geometric Momentum (IGM), which delivers an out-of-sample\n<\/div>\n<div>\n Sharpe ratio of 0.847 across 17 ETFs spanning four asset classes (2014-2025), compared\n<\/div>\n<div>\n with 0.614 for the standard time-series momentum benchmark. Strikingly, the IGM and\n<\/div>\n<div>\n Kalman-filter TSMOM portfolios converge statistically (p = 0.743 on a paired return dif-\n<\/div>\n<div>\n ferential test), suggesting that both the geometric and state-space approaches detect the\n<\/div>\n<div>\n same latent signal. A certainty-equivalent return analysis segments the investor universe:\n<\/div>\n<div>\n standard TSMOM dominates for low risk aversion (\u03b3 \u2264 2), IGM for institutional risk\n<\/div>\n<div>\n preferences (\u03b3 = 3-10), and Kalman-filter TSMOM for the most risk-averse allocators\n<\/div>\n<div>\n (\u03b3 \u2265 15). We establish boundary conditions by demonstrating that the \u03a6 diagnostic\n<\/div>\n<div>\n loses predictive power on futures markets, where roll-yield contamination attenuates the\n<\/div>\n<div>\n relationship between directional purity and forward returns. The framework contributes\n<\/div>\n<div>\n a new lens through which practitioners can evaluate when and why momentum signals\n<\/div>\n<div>\n carry information, rather than merely whether they do.\n<\/div><\/jats:p>","DOI":"10.2139\/ssrn.7585439","type":"posted-content","created":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T19:36:21Z","timestamp":1791488181000},"source":"Crossref","is-referenced-by-count":0,"title":["Information Geometry and Time-Series Momentum:A Riemannian Framework for Signal Quality"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-9343-2895","authenticated-orcid":true,"given":"Sparsh","family":"Patel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T19:36:21Z","timestamp":1791488181000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=7585439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.7585439","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}