Paper: arXiv 2609.02525

Authors: Alejandro Rodriguez Dominguez

Abstract

This paper develops a mechanism through which costly changes in the representations used for portfolio choice can contribute to persistent signed order flow. Heterogeneous switching thresholds and opportunity volatility generate heterogeneous residence times, and renewal aggregation maps their execution-weighted tail into the decay of aggregate flow covariance. Under common execution weights, the same tail determines the exponent of representation-spell durations, the order-flow memory exponent, and the horizon at which finite-market scaling must end. First-passage renewal analysis establishes these joint restrictions. Structural simulations recover them from realized paths, quantify the distortion created by mismatched weights, and show how finite cross sections shorten the usable inference horizon. The resulting empirical protocol converts an aggregate persistence fit into cross-dataset restrictions that can determine whether a duration-based kernel is suitable for a separate execution-cost model.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical framework involving first-passage renewal analysis and stochastic processes to model order flow. While it outlines an empirical protocol and discusses structural simulations, the excerpt doesn’t detail specific datasets or extensive backtesting results, suggesting a strong theoretical foundation with a clear path to empirical validation. The novelty lies in linking portfolio switching costs to long-memory order flow through a rigorous mathematical derivation.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Persistent Signed Order Flow] --> B{Mechanism: Costly Representation Changes};
    B --> C{Methodology: Heterogeneous Switching & Renewal Aggregation};
    C --> D[Inputs: Heterogeneous Switching Thresholds, Opportunity Volatility, Execution Weights];
    D --> E{Computational Processes: First-Passage Renewal Analysis, Structural Simulations};
    E --> F[Key Findings: Joint Restrictions on Exponents, Inference Horizon Limits, Empirical Protocol for Kernel Suitability];

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and 26 more
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  2. Theory for Long Memory in Supply and Demand (2005) — link
  3. Scaling Laws of Strategic Behavior and Size Heterogeneity in Agent Dynamics (2008) — link
  4. Market Impact and Trading Profile of Hidden Orders in Stock Markets (2009) — link
  5. Why Is Equity Order Flow So Persistent? (2015) — link
  6. Inferring Microscopic Financial Information from the Long Memory in Market-Order Flow: A Quantitative Test of the Lillo-Mike-Farmer Model (2023) — link
  7. Exact Solution to a Generalised Lillo–Mike–Farmer Model with Heterogeneous Order-Splitting Strategies — → 2306.13378
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  19. Rough Fractional Diffusions as Scaling Limits of Nearly Unstable Heavy Tailed Hawkes Processes (2016) — link
  20. Long Memory and Regime Switching (2001) — link
  21. A Unified Theory of Order Flow, Market Impact, and Volatility (2026) — link
  22. The Subtle Interplay Between Square-Root Impact, Order Imbalance and Volatility: A Unifying Framework (2025) — link
  23. Dynamic Causal Portfolio Choice: Hedging the Rotation of the Common-Driver Manifold (2026) — link
  24. The Market’s Conditioning Representation: Equilibrium, Crowding, and Convention Multiplicity (2026) — link
  25. Uniform Inference and Certified Capacity at a Reflexive Stability Boundary — → 2609.02535
  26. Reflexivity from Hierarchical Causality (2026)

2 of 34 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.