Scaling and memory in the non-poisson process of limit order cancelation

摘要

The order submission and cancelation processes are two crucial aspects in theprice formation of stocks traded in order-driven markets. We investigate thedynamics of order cancelation by studying the statistical properties ofinter-cancelation durations defined as the waiting times between consecutiveorder cancelations of 22 liquid stocks traded on the Shenzhen Stock Exchange ofChina in year 2003. Three types of cancelations are considered includingcancelation of any limit orders, of buy limit orders and of sell limit orders.We find that the distributions of the inter-cancelation durations of individualstocks can be well modeled by Weibulls for each type of cancelation and thedistributions of rescaled durations of each type of cancelations exhibit ascaling behavior for different stocks. Complex intraday patterns are alsounveiled in the inter-cancelation durations. The detrended fluctuation analysis(DFA) and the multifractal DFA show that the inter-cancelation durationspossess long-term memory and multifractal nature, which are not influenced bythe intraday patterns. No clear crossover phenomenon is observed in thedetrended fluctuation functions with respect to the time scale. These findingsindicate that the cancelation of limit orders is a non-Poisson process, whichhas potential worth in the construction of order-driven market models.