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Order cancellation process plays a crucial role in the dynamics of priceformation in order-driven stock markets and is important in the constructionand validation of computational finance models. Based on the order flow data of18 liquid stocks traded on the Shenzhen Stock Exchange in 2003, we investigatethe empirical statistical properties of inter-cancellation durations in unitsof events defined as the waiting times between two consecutive cancellations.The inter-cancellation durations for both buy and sell orders of all the stocksfavor a $q$-exponential distribution when the maximum likelihood estimationmethod is adopted; In contrast, both cancelled buy orders of 6 stocks andcancelled sell orders of 3 stocks prefer Weibull distribution when thenonlinear least-square estimation is used. Applying detrended fluctuationanalysis (DFA), centered detrending moving average (CDMA) and multifractaldetrended fluctuation analysis (MF-DFA) methods, we unveil that theinter-cancellation duration time series process long memory and multifractalnature for both buy and sell cancellations of all the stocks. Our findings showthat order cancellation processes exhibit long-range correlated burstybehaviors and are thus not Poissonian.

Empirical properties of inter-cancellation durations in the Chinese stock market