Modeling High Frequency Market Order Dynamics Using Self-Excited Point Process

This paper extends the self-excited point process framework to model conditional arrival intensities of buy and sell orders of listed stocks. The cross-excitation of market orders is modeled explicitly such that buy size and buy side order book cumulative volume can affect the sell order intensity, and vice versa. Different variations of the framework are estimated by using method of maximum likelihood estimation, using a recursive application of the log-likelihood functions derived in this paper. Results indicate that by incorporating an order imbalance measure related to the probability weighted cumulative queue volume at the bid and ask sides of the market, one can improve the overall model goodness-of-fit significantly