  We show that multivariate Hawkes processes coupled with the nonparametric
estimation procedure first proposed in Bacry and Muzy (2015) can be
successfully used to study complex interactions between the time of arrival of
orders and their size, observed in a limit order book market. We apply this
methodology to high-frequency order book data of futures traded at EUREX.
Specifically, we demonstrate how this approach is amenable not only to analyze
interplay between different order types (market orders, limit orders,
cancellations) but also to include other relevant quantities, such as the order
size, into the analysis, showing also that simple models assuming the
independence between volume and time are not suitable to describe the data.
