Can we infer microscopic financial information from the long memory in market-order flow?: a quantitative test of the Lillo-Mike-Farmer model

TL;DR

This study provides the first quantitative validation of the Lillo-Mike-Farmer model by analyzing nine years of high-resolution trading data, confirming that microscopic order-splitting behavior explains long memory in market order flow.

Contribution

It offers the first direct empirical validation of the LMF model linking microscopic trader behavior to macroscopic market order correlations.

Findings

Metaorder-length distribution follows a power-law with exponent consistent with model predictions.

Order-splitting traders significantly contribute to long-range correlations in order flow.

The LMF model accurately predicts the relationship between microscopic and macroscopic order flow properties.

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 $\gamma$, such that $C(\tau) \propto \tau^{-\gamma}$ for large time-lag $\tau$. 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 $P(L)\propto L^{-\alpha-1}$ as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation: $\gamma \approx \alpha - 1$. 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.