Statistical Analysis for Partially-Observed Markov Processes with Marked Point Process Observations

University Of Missouri-Kansas City, Columbia MO

Investigators

Abstract

The proposed research, involving stochastic differential equation models, aims at the analysis of ultra high-frequency data (UHF), which are marked point process (MPP) observations. It has an array of applications in finance, and stochastic control and filtering. With harnessing newly available Graphics Processing Units (GPU) supercomputing power in mind and targeting benchmark stochastic volatility and Levy models, the first objective is to develop new uniformly consistent recursive algorithms via Bayesian Inference via Filtering Equations (BIFE) for propagating and updating joint conditional measures such as joint posterior distributions. The new recursive algorithms, which numerically solve the stochastic partial differential equations (SPDEs), are suitable for GPU computing, because the algorithms can not only be parallelized for computation, but also be partitioned for memory storage in each CPU. Moreover, the new algorithms provide additional many-fold increase in computing power due to the advantage of implicit methods over explicit methods. Combining GPU computing and gains from advances in numerical algorithms, this project carries out real-time tracking of stochastic volatility and real-time Bayesian model selections over sophisticated benchmark financial models for streaming UHF data. Electronic trading in all major world financial markets has routinely generated streams of UHF data. UHF data have spurred interest in empirical market microstructure and present new and interesting challenges that are essential to comprehend market microstructure, to monitor and regulate markets, and to conduct risk management. Theoretical, computational, and implementation issues for the estimation and applications of these models will be investigated. This project trains interdisciplinary Ph.D students with co-disciplines in Economics, develops a new graduate course, and produces a research monograph on this topic. The PI works closely with both undergraduate and graduate students, creates illustrative and research data sets, and develops publicly available software.