Inferring Microscopic Financial Information from the Long Memory in Market-Order Flow: A Quantitative Test of the...

Area of Science:

• Econophysics
• Market Microstructure
• Quantitative Finance

Background:

• Financial markets exhibit long-range correlation (LRC) in order flow, characterized by persistent order sign autocorrelation functions (ACF).
• The Lillo, Mike, and Farmer (LMF) model hypothesizes that this macroscopic correlation stems from microscopic order-splitting behavior of individual traders.
• Direct quantitative validation of the LMF model has been lacking due to the need for high-resolution, large-scale microscopic trading data.

Purpose of the Study:

• To provide the first quantitative validation of the LMF model's prediction relating microscopic order-splitting to macroscopic market correlations.
• To analyze a large, high-resolution dataset from the Tokyo Stock Exchange to observe and measure individual trader behavior.
• To bridge the gap between theoretical hypotheses in econophysics and empirical evidence in market microstructure.

Main Methods:

• Analysis of a comprehensive nine-year microscopic dataset from the Tokyo Stock Exchange.
• Statistical clustering to classify traders into 'order-splitting' and 'random' groups.
• Direct measurement of metaorder-length distributions P(L) ∝ L^{-α-1} and comparison with the ACF power-law exponent γ (γ ≈ α-1).

Main Results:

• The study provides the first direct, quantitative validation of the LMF model's prediction (γ ≈ α-1).
• Empirical data from the Tokyo Stock Exchange aligns quantitatively with the theoretical predictions of the LMF model.
• The research demonstrates that microscopic financial information, such as the number of order-splitting traders, can be inferred from macroscopic LRC in the ACF.

Conclusions:

• The findings offer solid empirical support for the microscopic order-splitting hypothesis as the driver of long-range correlation in financial markets.
• This research resolves a long-standing problem in econophysics and market microstructure by quantitatively linking micro and macro market dynamics.
• The study highlights the potential for inferring detailed trader behavior from observable market correlations.