Conjecture on overestimation of child-order triggering by statistically calibrated impact models

Prove or refute the conjecture that statistically calibrated impact models of joint price–order flow dynamics overestimate the positive triggering effect that a child order has on market order flow, with the proposed explanation grounded in the Lillo–Mike–Farmer model of autocorrelated order flow arising from superposed metaorders.

Background

The paper compares impact trajectories inferred from public data via econometric and machine learning models with those observed in proprietary metaorder executions, finding discrepancies such as near-linear growth during execution and limited reversion after completion. To explain this, the authors posit that models calibrated on public data misattribute persistent autocorrelation to reactive triggering, whereas the Lillo–Mike–Farmer framework suggests order flow persistence mainly originates from concurrent, independent metaorder executions.

Validating or refuting this conjecture is central to reconciling public-data-based models with empirical metaorder behavior and would guide the design of models (such as the modified TIM with parameter α) that more accurately separate direct price impact from induced market order flow.