  This paper extends the analysis of Muni Toke and Yoshida (2020) to the case
of marked point processes. We consider multiple marked point processes with
intensities defined by three multiplicative components, namely a common
baseline intensity, a state-dependent component specific to each process, and a
state-dependent component specific to each mark within each process. We show
that for specific mark distributions, this model is a combination of the ratio
models defined in Muni Toke and Yoshida (2020). We prove convergence results
for the quasi-maximum and quasi-Bayesian likelihood estimators of this model
and provide numerical illustrations of the asymptotic variances. We use these
ratio processes in order to model transactions occuring in a limit order book.
Model flexibility allows us to investigate both state-dependency (emphasizing
the role of imbalance and spread as significant signals) and clustering.
Calibration, model selection and prediction results are reported for
high-frequency trading data on multiple stocks traded on Euronext Paris. We
show that the marked ratio model outperforms other intensity-based methods
(such as "pure" Hawkes-based methods) in predicting the sign and aggressiveness
of market orders on financial markets.
