Switching Frictions, Heterogeneous Trading Horizons, and Long-Memory Order Flow

Battle Count: 99

Highly relevant to quantitative trading. The paper provides a structural mechanism for order-flow persistence that directly informs execution-cost models, algorithmic trading strategy design, and capacity estimation. The joint duration-flow-cutoff restrictions offer a falsifiable test for whether representation residence contributes incremental explanatory power beyond order splitting. The empirical protocol (Table 2) provides actionable conditions for admissibility of persistence kernels in execution-cost models. However, the paper is primarily theoretical and requires institution-specific portfolio-level data for empirical validation, limiting immediate practical deployment.

High complexity. The theoretical framework requires expertise in renewal theory, regular variation, first-passage times of reflected Brownian motion, Breiman's product lemma, and Karamata's theorem. The simulation protocol involves sampling from the exponential-product representation of sech(√2s), equilibrium residual-life distributions, and Poisson execution processes. Empirical implementation requires account-level representation tracking, execution-weighted tail estimation, held-out covariance estimation, and metaorder reconstruction for confound control. The mathematical machinery (Theorems 4, 7, 8) is non-trivial and requires careful attention to the order of limits (cross-sectional before long-lag).

The paper provides a complete simulation protocol including random seed (260902), explicit sampling procedures (48-component sech representation, gamma remainder, equilibrium residual draws), parameter values for all experiments, and detailed estimation procedures (Hill estimator with 8% top fraction, log-log regression over lags 24-256). However, no code repository is provided, and the empirical protocol requires proprietary portfolio-level data not publicly available. The theoretical proofs are fully self-contained in appendices.