  The Mike-Farmer (MF) model was constructed empirically based on the
continuous double auction mechanism in an order-driven market, which can
successfully reproduce the cubic law of returns and the diffusive behavior of
stock prices at the transaction level. However, the volatility (defined by
absolute return) in the MF model does not show sound long memory. We propose a
modified version of the MF model by including a new ingredient, that is, long
memory in the aggressiveness (quantified by the relative prices) of incoming
orders, which is an important stylized fact identified by analyzing the order
flows of 23 liquid Chinese stocks. Long memory emerges in the volatility
synthesized from the modified MF model with the DFA scaling exponent close to
0.76, and the cubic law of returns and the diffusive behavior of prices are
also produced at the same time. We also find that the long memory of order
signs has no impact on the long memory property of volatility, and the memory
effect of order aggressiveness has little impact on the diffusiveness of stock
prices.
