Abstract
In this chapter, particle Markov Chain Monte Carlo (PMCMC) method is applied to estimate ultra-high frequency data models. The class of models is proposed by Zeng (2003), who considers the explicit structure of market microstructure noise. Although the model is able to capture stylized facts of tick data, the nonlinear state-space model structure makes parameter estimation a challenge. We use PMCMC to estimate a couple models when the underlying intrinsic value processes follow a geometric Brownian motion or a jump-diffusion process, under 1/8 and 1/100 tick size rules. Moreover, some numeric methods that are able to enhance the algorithm efficiency are discussed. Numerical studies through simulation and real data show that PMCMC method is able to yield reasonable estimates for model parameters.
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