Event-Time Order-Flow Memory, Operational-Time Impact, and Subordinated Market Observables

RESUMO

We consider two canonical market-microstructure regularities: the long-memory of trade signs and the square-root law of meta-order impact. The point is not to propose new empirical laws, but to separate the clocks on which existing laws are defined. The sign-memory is an event-time statement about the ordering and fragmentation of hidden orders. The impact law is an operational-time front motion in a locally linear latent order book. Starting from a discrete-time random-walk bid/ask reaction-diffusion order book with an event clock, we identify an imbalance reduction, derive the equations of impact in operational-time regime, and then subordinate both sign and observables to calendar time. Fractional or tempered clock effects enter through this event-to-calendar projection, different from impact mechanism. This gives a compact clock-aware framework where persistence, impact, and anomalous calendar-time effects appear as distinct but compatible consequences of a common order-book representation.