Fall Seminar Series - October 14, 2004
University of Minnesota
School of Statistics
College of Liberal Arts
Filtering
with a Marked Point Process Observation:
Applications to the Econometrics of Ultra-High-Frequency Data
Yong Zeng
Department of Mathematics and Statistics
University of Missouri
Thursday, October 14, 2004
NOTE NEW TIME
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
Ultra-high-frequency
(UHF) data 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 will be established. Two general approaches for
constructing algorithms will be discussed. One approach is Kushner's
Markov chain approximation method, and the other is Sequential
Monte Carlo method or particle filtering method. Some
simulation
and real data examples will be provided.