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

¹ School of Business, East China University of Science and Technology - Shanghai 200237, China
² School of Science, East China University of Science and Technology - Shanghai 200237, China
³ Research Center for Econophysics, East China University of Science and Technology - Shanghai 200237, China
⁴ College of Management and Economics, Tianjin University - Tianjin 300072, China

^a wxzhou@ecust.edu.cn

Received: 13 January 2012
Accepted: 3 April 2012

Abstract

Understanding the statistical properties of recurrence intervals (also termed return intervals in econophysics literature) 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 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.