  We introduce a Cox-type model for relative intensities of orders flows in a
limit order book. The model assumes that all intensities share a common
baseline intensity, which may for example represent the global market activity.
Parameters can be estimated by quasi likelihood maximization, without any
interference from the baseline intensity. Consistency and asymptotic behavior
of the estimators are given in several frameworks, and model selection is
discussed with information criteria and penalization. The model is well-suited
for high-frequency financial data: fitted models using easily interpretable
covariates show an excellent agreement with empirical data. Extensive
investigation on tick data consequently helps identifying trading signals and
important factors determining the limit order book dynamics. We also illustrate
the potential use of the framework for out-of-sample predictions.
