Computational Experiments Successfully Predict the Emergence of Autocorrelations in Ultra-High-Frequency Stock Returns

Social and economic systems are complex adaptive systems, in which heterogenous agents interact and evolve in a self-organized manner, and macroscopic laws emerge from microscopic properties. To understand the behaviors of complex systems, computational experiments based on physical and mathematical models provide a useful tools. Here, we perform computational experiments using a phenomenological order-driven model called the modified Mike–Farmer (MMF) to predict the impacts of order flows on the autocorrelations in ultra-high-frequency returns, quantified by Hurst index $$H_r$$ H r . Three possible determinants embedded in the MMF model are investigated, including the Hurst index $$H_s$$ H s of order directions, the Hurst index $$H_x$$ H x and the power-law tail index $$\alpha _x$$ α x of the relative prices of placed orders. The computational experiments predict that $$H_r$$ H r is negatively correlated with $$\alpha _x$$ α x and $$H_x$$ H x and positively correlated with $$H_s$$ H s . In addition, the values of $$\alpha _x$$ α x and $$H_x$$ H x have negligible impacts on $$H_r$$ H r , whereas $$H_s$$ H s exhibits a dominating impact on $$H_r$$ H r . The predictions of the MMF model on the dependence of $$H_r$$ H r upon $$H_s$$ H s and $$H_x$$ H x are verified by the empirical results obtained from the order flow data of 43 Chinese stocks.