  We propose a general framework to describe the impact of different events in
the order book, that generalizes previous work on the impact of market orders.
Two different modeling routes can be considered, which are equivalent when only
market orders are taken into account. One model posits that each event type has
a temporary impact (TIM). The "history dependent impact" model (HDIM), on the
other hand, assumes that only price-changing events have a direct impact,
itself modulated by the past history of all events through an "influence
matrix" that measures how much, on average, an event of a given type affects
the immediate impact of a price-changing event of the same sign in the future.
We find in particular that aggressive market orders tend to reduce the impact
of further aggressive market orders of the same sign (and increase the impact
of aggressive market orders of opposite sign). We discuss the relative merits
of TIM and HDIM, in particular concerning their ability to reproduce accurately
the price diffusion pattern. We find that in spite of theoretical
inconsistencies, TIM appears to fare better than HDIM when compared to
empirical data. We ascribe this paradox to an uncontrolled approximation used
to calibrate HDIMs, calling for further work on this issue.
