Ultra-high-frequency (UHF) data, arisen from financial marktes, is naturally modeled as a marked point process (MPP). In this talk, we propose a general filtering model for UHF data. The statistical foundations of the proposed model - likelihoods, posterior, likelihood ratios and Bayes factors - are studied. They are characterized by stochastic differential equations such as filtering equations. Convergence theorems for consistent, efficient algorithms are established. Two general approaches for constructing algorithms are discussed. One approach is Kushner's Markov chain approximation method, and the other is Sequential Monte Carlo method or particle filtering method. Simulation and real stock price data examples are provided.
Group for Research in Decision Analysis