  We propose an actionable calibration procedure for general Quadratic Hawkes
models of order book events (market orders, limit orders, cancellations). One
of the main features of such models is to encode not only the influence of past
events on future events but also, crucially, the influence of past price
changes on such events. We show that the empirically calibrated quadratic
kernel is well described by a diagonal contribution (that captures past
realised volatility), plus a rank-one "Zumbach" contribution (that captures the
effect of past trends). We find that the Zumbach kernel is a power-law of time,
as are all other feedback kernels. As in many previous studies, the rate of
truly exogenous events is found to be a small fraction of the total event rate.
These two features suggest that the system is close to a critical point -- in
the sense that stronger feedback kernels would lead to instabilities.
