Yong Zeng (University of Missouri, Kansas City)

Abstract:

In this talk, we propose a general filtering model with marked Poisson process observations for financial UHF data. The model can allow stochastic volatility as well as inputs from other observable factors such as signed order flow, and encompasses important existing models. The statistical foundations of the proposed model - likelihoods, posterior, likelihood ratios and Bayes factors - are studied. They are characterized by stochastic partial differential equations such as filtering equations. Bayesian inference (estimation and model selection) via filtering is studied. Convergence theorems for consistent, efficient algorithms are established. Two general approaches for constructing algorithms are discussed. One approach is Markov chain approximation method, and the other is sequential Monte Carlo or particle filtering. If time permits, examples of simulation, stock price and treasury data would be provided.