  Order cancellation process plays a crucial role in the dynamics of price
formation in order-driven stock markets and is important in the construction
and validation of computational finance models. Based on the order flow data of
18 liquid stocks traded on the Shenzhen Stock Exchange in 2003, we investigate
the empirical statistical properties of inter-cancellation durations in units
of events defined as the waiting times between two consecutive cancellations.
The inter-cancellation durations for both buy and sell orders of all the stocks
favor a $q$-exponential distribution when the maximum likelihood estimation
method is adopted; In contrast, both cancelled buy orders of 6 stocks and
cancelled sell orders of 3 stocks prefer Weibull distribution when the
nonlinear least-square estimation is used. Applying detrended fluctuation
analysis (DFA), centered detrending moving average (CDMA) and multifractal
detrended fluctuation analysis (MF-DFA) methods, we unveil that the
inter-cancellation duration time series process long memory and multifractal
nature for both buy and sell cancellations of all the stocks. Our findings show
that order cancellation processes exhibit long-range correlated bursty
behaviors and are thus not Poissonian.
