Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mike-Farmer (LMF) order-splitting theory. However, quantitative tests of this theory have historically relied on proprietary datasets with trader identifiers, limiting reproducibility and cross-market validation. We show that the LMF theory can be validated using publicly available Johannesburg Stock Exchange (JSE) data by leveraging recently developed methods for reconstructing synthetic metaorders. We demonstrate the validation using 3 years of Transaction and Quote Data (TAQ) for the largest 100 stocks on the JSE when assuming that there are either N=50 or N=150 effective traders managing metaorders in the market.

翻译：金融市场中的市场订单流呈现出长程相关性，这是金融市场中一个广为人知的典型事实。对于这一典型事实，一个流行的假说源于Lillo-Mike-Farmer（LMF）订单拆分理论。然而，历史上对该理论的定量检验依赖于包含交易者标识符的专有数据集，这限制了其可重复性和跨市场验证。我们证明，通过利用最近开发的合成元订单重构方法，可以使用公开的约翰内斯堡证券交易所（JSE）数据来验证LMF理论。我们利用JSE上最大的100只股票为期3年的交易与报价数据（TAQ）进行了验证，假设市场中有N=50或N=150个有效交易者在管理元订单。