High frequency dynamics of order flow

In this paper, we focus on the high frequency dynamics of limit order flow and market order flow. We compared the fitting performance of different models for the inter-arrival time of the order flow, including exponential distribution, gamma distribution and power law. We then studied the dependence of the placement of these two order flows, which can be captured by the self-excitation effect and mutual-excitation effect of Hawkes process. We also introduced a new model which combines the Hawkes features with the gamma distribution.\ud \ud Key words: High frequency dynamics; order flow; market microstructure; maximum likelihood estimation; Hawkes process; Hawkes-Gamma distribution