In financial markets, the market-order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign autocorrelation function (ACF) 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 behavior at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behavior, 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 behavior of all individual traders. Here we present the first quantitative validation of this LMF prediction by analyzing 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. We also discuss the estimation of the total number of the order-splitting traders from the ACF prefactor, showing that microscopic financial information can be inferred from the LRC in the ACF. Our Letter provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure.

中文翻译：

---

从市场订单流的长期记忆中推断微观金融信息：Lillo-Mike-Farmer 模型的定量检验

在金融市场中，市场秩序信号表现出很强的持久性，被广泛称为订单流的长期相关性（LRC）；具体来说，符号自相关函数（ACF）显示具有幂律指数的长记忆$\gamma$，使得$C（\tau ）\propto {\tau }^{-\gamma }$对于大时滞$\tau$。最有希望的微观假设之一是个体交易者层面的订单分割行为。事实上，Lillo、Mike 和 Farmer (LMF) 在 2005 年引入了一个简单的序分裂行为微观模型，该模型预测宏观符号相关性与元序的微观分布定量相关。虽然这一假设一直是经济物理学争论的核心问题，但它的直接定量验证一直缺失，因为它需要高分辨率的大型微观数据集来观察所有个体交易者的订单拆分行为。在这里，我们通过分析东京证券交易所市场九年多来的大型微观数据集，首次对 LMF 预测进行了定量验证。在将所有交易者分类为订单分割交易者或随机交易者作为统计聚类时，我们直接测量了元订单长度分布$磷（L）\propto L^{-\alpha -1}$作为LMF模型的微观参数，检验了宏观阶次相关性的理论预测$\gamma \approx \alpha -1$。我们发现，即使在定量层面上，LMF 预测也与实际数据相符。我们还讨论了从 ACF 前因子中对分单交易者总数的估计，表明可以从 ACF 中的 LRC 推断出微观金融信息。我们的信为微观模型提供了第一个坚实的支持，并直接解决了经济物理学和市场微观结构领域长期存在的问题。