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Understanding the statistical properties of recurrence intervals of extremeevents is crucial to risk assessment and management of complex systems. Theprobability distributions and correlations of recurrence intervals for manysystems have been extensively investigated. However, the impacts of microscopicrules of a complex system on the macroscopic properties of its recurrenceintervals are less studied. In this Letter, we adopt an order-driven stockmarket model to address this issue for stock returns. We find that thedistributions of the scaled recurrence intervals of simulated returns have apower law scaling with stretched exponential cutoff and the intervals possessmultifractal nature, which are consistent with empirical results. We furtherinvestigate the effects of long memory in the directions (or signs) andrelative prices of the order flow on the characteristic quantities of theseproperties. It is found that the long memory in the order directions (Hurstindex $H_s$) has a negligible effect on the interval distributions and themultifractal nature. In contrast, the power-law exponent of the intervaldistribution increases linearly with respect to the Hurst index $H_x$ of therelative prices, and the singularity width of the multifractal naturefluctuates 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 ofthe recurrence intervals. Our results indicate that the nontrivial propertiesof the recurrence intervals of returns are mainly caused by traders' behaviorsof persistently placing new orders around the best bid and ask prices.

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