Paper: arXiv 2611.10574

Authors: Shunta Fujiwara, Yuki Sato, Kiyoshi Kanazawa

Abstract

Despite the long memory of market-order flow, price dynamics remain diffusive—a seemingly paradoxical coexistence known in econophysics as the diffusivity puzzle. The propagator model has long been regarded as a promising solution: price impact decays in time, finely balanced against the order-flow memory, and propagators inferred from data have been reported to be consistent with this fine balance. Here we prove a no-go theorem: asymptotic impact decay is not statistically identifiable by propagator estimation, since for diffusive prices the fine-tuned decay is returned whether or not the true impact decays. It rests on universal theorems for the Wiener–Hopf deconvolution by which propagators are inferred under long-memory order flow: (i) the inferred propagator is necessarily transient, even when the true impact is permanent; (ii) under a mild condition, it decays with the fine-balance exponent, fixed by the order-flow autocorrelation alone. The fine-tuned decay is thus a property of the deconvolution, not evidence of impact decay. We demonstrate this with an exactly solvable null model that retains order splitting and the square-root law but whose impact is strictly permanent: the inferred propagator shows an artificial fine-tuned decay although the true impact never decays. Nonlinear propagator estimation, being of Wiener–Hopf type, is subject to the same theorems whenever true metaorders have long memory.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly mathematical proof (no-go theorem) regarding the identifiability of price-impact decay. While it uses a null model for demonstration, it lacks extensive empirical backtesting or real-world data validation, focusing more on theoretical implications. The novelty lies in challenging a widely accepted interpretation within econophysics.

Research Flowchart

  flowchart TD
    A[Research Goal/Question: Is price-impact decay statistically identifiable by propagator estimation given long-memory order flow and diffusive prices?] --> B{Methodology: Theoretical Proof (No-Go Theorem)};
    B --> C{Core Process: Wiener-Hopf Deconvolution Analysis};
    C --> D[Inputs/Assumptions: Long-memory order flow, Diffusive prices (from "diffusivity puzzle")];
    D --> E{Computational Demonstration: Exactly solvable null model (permanent impact, order splitting, square-root law)};
    E --> F[Key Finding 1: Inferred propagator is necessarily transient, even if true impact is permanent];
    F --> G[Key Finding 2: Inferred propagator decays with fine-balance exponent, fixed by order-flow autocorrelation];
    G --> H[Outcome: Fine-tuned decay is property of deconvolution, not evidence of true impact decay. Price impact decay is not statistically identifiable by propagator estimation.];