The authors model trades-through, i.e. transactions that reach at least the second level of limit orders in an order book. Using tick-by-tick data on Euronext-traded stocks, they show that a simple bivariate Hawkes process fits nicely their empirical observations of trades-through. The authors show that the cross-influence of bid and ask trades-through is weak.
The data set for this article can be found at: http://hdl.handle.net/1902.1/18359