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We construct a general procedure for the Quasi Likelihood Analysis applied toa multivariate point process on the real half line in an ergodic framework.More precisely, we assume that the stochastic intensity of the underlying modelbelongs to a family of processes indexed by a finite dimensional parameter.When a particular family of laws of large numbers applies to those processes,we establish the consistency, the asymptotic normality and the convergence ofmoments of both the Quasi Maximum Likelihood estimator and the Quasi Bayesianestimator. In addition, we illustrate our main results by showing how they canbe applied to various Limit Order Book models existing in the literature. Inparticular, we address the fundamental cases of Markovian models andexponential Hawkes process-based models.

Statistical Inference for Ergodic Point Processes and Application to Limit Order Book