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

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.

arXiv comment6 EPL pages including 6 figures

References in corpus (35)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Improved surrogate data for nonlinearity tests
• Detecting Long-range Correlations with Detrended Fluctuation Analysis
• Effect of Trends on Detrended Fluctuation Analysis
• Effect of nonstationarities on detrended fluctuation analysis
• Cross-correlations between volume change and price change
• Magnitude and Sign Correlations in Heartbeat Fluctuations
• Effect of nonlinear filters on detrended fluctuation analysis
• The components of empirical multifractality in financial returns
• Simple model of a limit order-driven market
• Recurrence time analysis, long-term correlations, and extreme events
• Common Scaling Patterns in Intertrade Times of U. S. Stocks
• Scaling and memory of intraday volatility return intervals in stock market
• Return interval distribution of extreme events and long term memory
• Emergence of long memory in stock volatility from a modified Mike-Farmer model
• Scaling in the distribution of intertrade durations of Chinese stocks
• Indication of multiscaling in the volatility return intervals of stock markets
• On the probability distribution of stock returns in the Mike-Farmer model
• Recurrence interval analysis of high-frequency financial returns and its application to risk estimation
• Multifactor Analysis of Multiscaling in Volatility Return Intervals
• Financial factor influence on scaling and memory of trading volume in stock market
• Statistical properties of volatility return intervals of Chinese stocks
• Scaling and Memory Effect in Volatility Return Interval of the Chinese Stock Market
• Volatility return intervals analysis of the Japanese market
• Scaling and memory in the return intervals of realized volatility
• Multiscaling behavior in the volatility return intervals of Chinese indices
• Scaling and memory in recurrence intervals of Internet traffic
• Recurrence interval analysis of trading volumes
• Extreme value statistics and return intervals in long-range correlated uniform deviates
• Return times for Stochastic processes with power-law scaling
• A Multi Agent Model for the Limit Order Book Dynamics
• Recurrence intervals between earthquakes strongly depend on history
• Distribution of Return Intervals of Extreme Events
• Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence
• On the properties of random multiplicative measures with the multipliers exponentially distributed

Cited by in corpus (13)

• Multifractal analysis of financial markets
• The fine-structure of volatility feedback I: multi-scale self-reflexivity
• Extreme value statistics and recurrence intervals of NYMEX energy futures volatility
• Computational experiments successfully predict the emergence of autocorrelations in ultra-high-frequency stock returns
• New approaches in agent-based modeling of complex financial systems
• Development of an agent-based speculation game for higher reproducibility of financial stylized facts
• A detailed heterogeneous agent model for a single asset financial market with trading via an order book
• Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets
• Empirical properties of inter-cancellation durations in the Chinese stock market
• On the long-term correlations and multifractal properties of electric arc furnace time series
• Self-reinforcing feedback loop in financial markets with coupling of market impact and momentum traders
• An empirical behavioural order-driven model with price limit rules
• Analysis of inter-transaction time fluctuations in the cryptocurrency market