{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:52:55Z","timestamp":1791553975162,"version":"4.3.4"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":62,"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:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We develop a structural econometric framework for identifying latent agent heterogeneity and time-varying participation rates from the temporal structure of high-frequency trading (HFT). We formulate a mean-field time-equilibrium model in which rationally inattentive agents optimally choose the timing of their actions, making the market clock an endogenous equilibrium object. Equilibrium in business time, combined with a locally scale-invariant representation of the market clock, yields a q-Weibull representation of calendar-time durations whose shape reflects the composition of heterogeneous market participants. We exploit this temporal structure to establish identification at three complementary levels. Identification does not require recovery of agent-specific utility functions or other structural primitives, and remains well defined under misspecification of the finite-dimensional representation of the latent equilibrium. The identified components yield an instantaneous Relative Proportion (\\(\\mathrm{iRP}\\)) of agent types, for which we develop estimation and inference. Unlike conventional composition measures based on temporally aggregated activity, \\(\\mathrm{iRP}\\) exploits duration-conditioned intensities and is therefore defined pointwise and can be aggregated over arbitrary horizons. We illustrate the framework by recovering the time-varying presence of informed trading and by constructing a local measure of HFT reflexivity that captures endogenous amplification across agent types. The latter is strongly associated with market stress and extreme market events.<\/jats:p>","DOI":"10.2139\/ssrn.7589386","type":"posted-content","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:29:52Z","timestamp":1791552592000},"source":"Crossref","is-referenced-by-count":0,"title":["The Tell-Tale Clock! 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