IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, VOL. 6, NO. 4, AUGUST 2012 381 Statistical Analysis and Agent-Based Microstructure Modeling of High-Frequency Financial Trading Linda Ponta, Member, IEEE, Enrico Scalas, Marco Raberto, and Silvano Cincotti Abstract—A simulation of high-frequency market data is per- formed with the Genoa Artificial Stock Market. Heterogeneous agents trade a risky asset in exchange for cash. Agents have zero intelligence and issue random limit or market orders depending on their budget constraints. The price is cleared by means of a limit order book. A renewal order-generation process is used having a waiting-time distribution between consecutive orders that follows a Weibull law, in line with previous studies. The simulation results show that this mechanism can reproduce fat-tailed distributions of returns without ad-hoc behavioral assumptions on agents. In the simulated trade process, when the order waiting-times are exponentially distributed, trade waiting times are exponentially distributed. However, if order waiting times follow a Weibull law, analogous results do not hold. These findings are interpreted in terms of a random thinning of the order renewal process. This behavior is compared with order and trade durations taken from real financial data. Index Terms—Artificial stock market, high-frequency financial time-series, random thinning, Weibull distribution. I. INTRODUCTION I N RECENT years, thanks to the availability of large databases of financial data, the statistical properties of high-frequency financial data and market microstructural prop- erties have been studied by means of different tools, including phenomenological models of price dynamics and agent-based market simulations [1]–[18]. Various studies on high-frequency econometrics appeared in the literature including the autore- gressive conditional duration models [19]–[23]. Among these approaches, agent-based based simulations [7], [8], [11]–[13] are particularly flexible as they allow the study of both the behavior of agents and the influence of market structures in a well-controlled way. Since the early 1990s, artificial financial markets based on interacting agents have been developed. It is Manuscript received June 30, 2011; revised October 21, 2011; accepted Oc- tober 27, 2011. Date of publication October 31, 2011; date of current version July 13, 2012. This work was supported in part by the University of Genoa and in part by the Italian Ministry of Education, University, and Research (MIUR). The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ali Akansu. L. Ponta, M. Raberto, and S. Cincotti are with the Research Center on Organ- ization, Economics, and Management (DOGE.I-CINEF), University of Genoa, 16145 Genova, Italy (e-mail: linda.ponta@unige.it; marco.raberto@unige.it; silvano.cincotti@unige.it). E. Scalas is with Department of Science and Advanced Technology, University of East Piedmont, 15121 Alessandria, Italy, and also with the BCAM—Basque Center for Applied Mathematics, 48160 Derio, Spain (e-mail: enrico.scalas@mfn.unipmn.it; escalas@bcamath.org). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTSP.2011.2174192 worth noting that besides some early Monte Carlo simulations (e.g., [24] and [25]), microscopic simulations of financial mar- kets initially aimed more to provide mechanisms for bubbles and crashes rather than to look at statistical features of the so generated time series. The first artificial market was built at the Santa Fe Institute [26]–[28]. It is characterized by heteroge- neous agents with limited rationality. While early attempts at microscopic simulations of financial markets appeared unable to account for the ubiquitous scaling laws of returns (and were, in fact, not devised to explain them), the recent models seem to be able to explain some of the statistical properties of financial data, but in most cases the attention is focused only on one styl- ized fact. Generally speaking, the objective of artificial markets is to reproduce the statistical features of the price process with minimal hypotheses about the intelligence of agents [29]. Sev- eral artificial markets populated with simple agents have been developed and have been able to reproduce some stylized facts, e.g., fat tails of returns and volatility autocorrelation [7], [8], [30]–[33]. For a detailed review of microscopic agent-based models of financial markets, see [34] and [35]. Stochastic models alternative to artificial markets have also been proposed, e.g., diffusive models, ARCH-GARCH models, stochastic volatility models, models based on fractional pro- cesses, models based on subordinate processes [36]–[42]. In particular, studies of stock markets vulnerability which utilize models of collective behavior of large group of agents have been proposed. This led to consider collective behavior that could reflect herding phenomena [36], [43], [44]. More recently, the role of heterogeneity, agents’ interactions and trade frictions on stylized facts of stock market returns have also been considered [45]. Here, the focus is on the influence of the double auction clearing mechanism where the price is fixed by the order book. An important variable is the order imbalance. Most existing studies analyze order imbalances around specific events or over short periods of time. For example, in [46] order imbalances are analyzed around the October 1987 crash. In [47], it is analyzed how order imbalances change the contemporaneous relation between stock volatility and volume using data for about six months. A large body of research examines the effect of the bid-ask spread and the order impact on the short-run behavior of prices [48]–[61]. Another important empirical variable is the waiting time be- tween two consecutive transactions [10], [62]. Empirically, in the market, during a trading day the activity is not constant [63] leading to fractal-time behavior [64], [65]. Due to the double auction mechanism, waiting times between two trades are themselves a stochastic variable [66]–[68]. They 1932-4553/$26.00 © 2011 IEEE