Order Flow and Autocorrelation in Ultra-High-Frequency Stock Returns

Summary

This study uses computational experiments with a modified Mike–Farmer order-driven model to examine how order flow shapes autocorrelation in ultra-high-frequency stock returns. It measures return dependence with the Hurst index and varies three order-flow properties: persistence in order direction, persistence in relative order prices, and the tail index of relative order prices.

The model predicts that return autocorrelation rises with persistence in order direction and falls with the other two properties. However, the authors find that order-direction persistence has the dominant effect, while the relative-price parameters have little influence. They compare these predictions with order-flow data from 43 Chinese stocks, reporting empirical support for the model’s predicted relationships involving order-direction and relative-price persistence. The results concern a particular phenomenological model and the studied stock sample; the excerpt does not establish how well the predictions generalize to other markets or explain the mechanisms behind the weak relative-price effects.

Key ideas

• The modified Mike–Farmer model links order-flow properties to ultra-high-frequency return autocorrelation.
• The study measures return dependence using the Hurst index.
• Persistent order directions have a positive and dominant modeled relationship with return autocorrelation.
• Relative order-price persistence and its tail index have negative but negligible modeled effects.
• Data from 43 Chinese stocks support some of the model’s predicted relationships.

Tags

# Computational experiments successfully predict the emergence of autocorrelations in ultra-high-frequency stock returns


# 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 $H_r$. Three possible determinants embedded in the MMF model are investigated, including the Hurst index $H_s$ of order directions, the Hurst index $H_x$ and the power-law tail index $α_x$ of the relative prices of placed orders. The computational experiments predict that $H_r$ is negatively correlated with $α_x$ and $H_x$ and positively correlated with $H_s$. In addition, the values of $α_x$ and $H_x$ have negligible impacts on $H_r$, whereas $H_s$ exhibits a dominating impact on $H_r$. The predictions of the MMF model on the dependence of $H_r$ upon $H_s$ and $H_x$ are verified by the empirical results obtained from the order flow data of 43 Chinese stocks.

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