Statistics and Its Interface

Volume 6 (2013)

Number 4

Bayes estimation via filtering equation through implicit recursive algorithms for financial ultra-high frequency data

Pages: 487 – 498

DOI: http://dx.doi.org/10.4310/SII.2013.v6.n4.a7

Authors

Brent Bundick (Department of Economics, Boston College, Boston, Massachusetts, U.S.A.)

Noah Rhee (Department of Mathematics and Statistics, University of Missouri, Kansas City, Missouri, U.S.A.)

Yong Zeng (Department of Mathematics and Statistics, University of Missouri, Kansas City, Missouri, U.S.A.)

Abstract

We review a recently proposed general partially-observed framework of Markov processes with marked point process observations for financial ultra-high frequency (UHF) data, and the related Bayes estimation via filtering equation (BEFE), a stochastic PDE approach. In this paper, we show how the BEFE through explicit recursive algorithms becomes bottlenecked when the tick size is reduced from $\$1/8$ to $\$1/100$, and we develop the BEFE through implicit recursive algorithms, greatly improving the computational efficiency. We demonstrate the substantial computation gained in implementing real-time BEFE for an illustrating but practical model using simulated data. The new implicit recursive algorithm is applied to a real stock price UHF data set, and is capable of producing real time Bayes parameter estimates of the model.

Keywords

Bayes estimation, implicit methods, marked point process, market microstructure noise, Markov chain approximation method, nonlinear filtering, partially observed model, ultra-high frequency data

2010 Mathematics Subject Classification

Primary 62F15, 62M05, 62P05. Secondary 60G55, 60H35, 65C60, 93E11.

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