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Abstract:
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Financial ultra-high-frequency data (UHF) are naturally modeled as a marked point process. We propose a general filtering model for UHF data allowing inputs from other observable factors. The model encompasses important existing models such as Exponential ACD models. 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. Bayesian inference via filtering is studied in detail. Simulation and real stock price data examples are provided, if time permits.
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