Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations

TL;DR

This study investigates how long memory in order flow influences the statistical properties of recurrence intervals of large price fluctuations in stock markets, revealing that relative price memory significantly affects these properties.

Contribution

It demonstrates that long memory in order directions has little effect, while memory in relative prices significantly impacts recurrence interval distributions and multifractal characteristics.

Findings

Power law scaling of recurrence intervals with stretched exponential cutoff

Linear increase of power-law exponent with Hurst index of relative prices

Constant multifractal singularity width when H_x<0.7

Abstract

Understanding the statistical properties of recurrence intervals of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have been extensively investigated. However, the impacts of microscopic rules of a complex system on the macroscopic properties of its recurrence intervals are less studied. In this Letter, we adopt an order-driven stock market model to address this issue for stock returns. We find that the distributions of the scaled recurrence intervals of simulated returns have a power law scaling with stretched exponential cutoff and the intervals possess multifractal nature, which are consistent with empirical results. We further investigate the effects of long memory in the directions (or signs) and relative prices of the order flow on the characteristic quantities of these properties. It is found that the long memory in the order directions (Hurst index $H_s$) has a negligible effect on the interval distributions and the multifractal nature. In contrast, the power-law exponent of the interval distribution increases linearly with respect to the Hurst index $H_x$ of the relative prices, and the singularity width of the multifractal nature fluctuates around a constant value when $H_x<0.7$ and then increases with $H_x$. No evident effects of $H_s$ and $H_x$ are found on the long memory of the recurrence intervals. Our results indicate that the nontrivial properties of the recurrence intervals of returns are mainly caused by traders' behaviors of persistently placing new orders around the best bid and ask prices.