Liquidity-Adjusted Signal Formation Under Transient Price Impact

This note examines the instability of signal persistence when transient impact kernels are misidentified as durable informational drift. Under a propagator-style decomposition, observed price continuation can be represented as a convolution of latent order-flow pressure, liquidity replenishment, and endogenous narrative reinforcement. The practical implication is not a directional rule, but a constraint on when apparent momentum should be interpreted as structurally supported rather than mechanically exhausted.

Price increments are modelled as dP_t = ∫_0^t G(t−s) dV_s + σ dB_t with G a transient propagator and V_t cumulative signed flow. The information component is the residual once G is identified via off-event windows.

When G is misspecified as instantaneous, mechanical replenishment after a liquidity shock is absorbed into the apparent direction of conviction. Conditional on event regimes, the inferred signal half-life is then systematically biased toward overconfidence in the first decile of the post-event window.

Signal classifications generated within minutes of a liquidity shock should be down-weighted by an estimate of impact-decay residual energy. We treat unreconciled propagator residuals as a hard constraint on signal confidence.

Decomposition is identified up to a normalization of the kernel and assumes flow telemetry that is rarely available cleanly outside venue-level data.