Paper: arXiv 2301.13505

Authors: Yuki Sato, Kiyoshi Kanazawa

Abstract

In financial markets, the market order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign correlation function displays long memory with power-law exponent $γ$, such that $C(τ) \propto τ^{-γ}$ for large time-lag $τ$. One of the most promising microscopic hypotheses is the order-splitting behaviour at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behaviour, which predicts that the macroscopic sign correlation is quantitatively associated with the microscopic distribution of metaorders. While this hypothesis has been a central issue of debate in econophysics, its direct quantitative validation has been missing because it requires large microscopic datasets with high resolution to observe the order-splitting behaviour of all individual traders. Here we present the first quantitative validation of this LFM prediction by analysing a large microscopic dataset in the Tokyo Stock Exchange market for more than nine years. On classifying all traders as either order-splitting traders or random traders as a statistical clustering, we directly measured the metaorder-length distributions $P(L)\propto L^{-α-1}$ as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation: $γ\approx α- 1$. We discover that the LMF prediction agrees with the actual data even at the quantitative level. Our work provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 9.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a landmark empirical validation of a fundamental econophysics theory using a massive 9-year proprietary dataset from the Tokyo Stock Exchange. By directly measuring individual trader metaorders to confirm the Lillo-Mike-Farmer model’s power-law scaling prediction, it resolves a major long-standing debate in market microstructure with high statistical rigor.

Research Flowchart

  flowchart TD
    A["<b>Research Question</b><br>Can microscopic order-splitting (LMF model) quantitatively explain macroscopic long-range correlation (LRC)?"] --> B["<b>Dataset</b><br>9+ years of high-resolution TSE microscopic data for all traders"]
    
    B --> C["<b>Trader Classification</b><br>Cluster traders into Order-Splitting Traders vs. Random Traders"]
    
    C --> D["<b>Microscopic Measurement</b><br>Extract metaorder-length distribution: <i>P(L) ∝ L<sup>-α-1</sup></i>"]
    
    D --> E["<b>Macroscopic Analysis & Validation</b><br>Calculate sign correlation exponent <i>γ</i> and test LMF prediction: <i>γ ≈ α - 1</i>"]
    
    E --> F["<b>Key Outcome</b><br>First direct quantitative validation of the LMF model, confirming order-splitting causes LRC"]