Monte Carlo likelihood inference for marked doubly stochastic Poisson processes with intensity driven by marked point processes

In recent years, marked point processes have found a natural application in the modeling of ultra-high-frequency financial data since they do not require the integration of the data which is usually needed by other modeling approaches. Among these processes, two main classes have so far been proposed to model financial data: the class of autoregressive conditional duration models of Engle and Russel and the broad class of doubly stochastic Poisson processes with marks. In this paper we consider a class of marked doubly stochastic Poisson processes in which the intensity is driven by another marked point process. In particular, we focus on an intensity with a shot noise form that can be interpreted in terms of the effect caused by news arriving on the market. For models in this class we study likelihood inferential procedures such as Monte Carlo likelihood and importance sampling Monte Carlo expectation maximization by making use of reversible jump Markov chain Monte Carlo algorithms.