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In this research, we focus on the order-splitting behavior. The ordersplitting is a trading strategy to execute their large potential metaorder intosmall pieces to reduce transaction cost. This strategic behavior is believed tobe important because it is a promising candidate for the microscopic origin ofthe long-range correlation (LRC) in the persistent order flow. Indeed, in 2005,Lillo, Mike, and Farmer (LMF) introduced a microscopic model of theorder-splitting traders to predict the asymptotic behavior of the LRC from themicroscopic dynamics, even quantitatively. The plausibility of this scenariohas been qualitatively investigated by Toth et al. 2015. However, no solidsupport has been presented yet on the quantitative prediction by the LMF modelin the lack of large microscopic datasets. In this report, we have provided thefirst quantitative statistical analysis of the order-splitting behavior at thelevel of each trading account. We analyse a large dataset of the Tokyo stockexchange (TSE) market over nine years, including the account data of traders(called virtual servers). The virtual server is a unit of trading accounts inthe TSE market, and we can effectively define the trader IDs by an appropriatepreprocessing. We apply a strategy clustering to individual traders to identifythe order-splitting traders and the random traders. For most of the stocks, wefind that the metaorder length distribution obeys power laws with exponent$\alpha$, such that $P(L)\propto L^{-\alpha-1}$ with the metaorder length $L$.By analysing the sign correlation $C(\tau)\propto \tau^{-\gamma}$, we directlyconfirmed the LMF prediction $\gamma \approx \alpha-1$. Furthermore, we discusshow to estimate the total number of the splitting traders only from public datavia the ACF prefactor formula in the LMF model. Our work provides the firstquantitative evidence of the LMF model.

Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years