JSM 2005 - Toronto

Abstract #302818

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 265
Type: Contributed
Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #302818
Title: Filtering with a Marked Point Process Observation: Applications to the Econometrics of Ultra-High-Frequency Data
Author(s): Yong Zeng*+
Companies: University of Missouri, Kansas City
Address: 5100 Rockhill Rd, Kansas City, MO, 64110, United States
Keywords: Ultra High Frequency Data ; Marked Point Process ; Filtering ; Sqquential Monte Carlo ; Bayesian Statistics ; Irregualarly-space time series
Abstract:

Ultra-high-frequency (UHF) data is naturally modeled as a marked point process (MPP). Even though econometricians model UHF data as a MPP, they view UHF data as an irregularly spaced time series. In this talk, we take the angle of probabilists and view UHF data as an observed sample path of a MPP. Then, we propose a general filtering model for UHF data where the signals are latent processes that can be observed only at random times and the observations are in a generic mark space with other observable factors. The statistical foundations of the proposed model---likelihoods, posterior, likelihood ratios, and Bayes factors---are studied. They all are of continuous time, of infinite dimension, and are characterized by stochastic differential equations such as filtering equations. These equations are derived. Mathematical foundations 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. Simulation and real data examples will be provided.

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Revised March 2005