Filtered Likelihood for Point Processes

Abstract

Point processes are used to model the timing of defaults, market transactions, births, unemployment and many other events. We develop and study likelihood estimators of the parameters of a marked point process and of incompletely observed explanatory factors that influence the arrival intensity and mark distribution. We establish an approximation to the likelihood and analyze the convergence and large-sample properties of the associated estimators. Numerical results highlight the computational efficiency of our estimators, and show that they can outperform EM Algorithm estimators.