Abstract for "Econometric Analysis via Filtering for Financial Ultra-High Frequency (UHF) Data" by Yong ZengWe propose a general nonlinear filtering framework with marked point process observations for financial UHF data. The signal contains an intrinsic value and related parameters and is modeled as a general Markov process. Trading times are driven by a generic point process, and the noise is described by a random transformation from the intrinsic value to trading price. Other observable variables (such as initiators of trade, and economic news) are allowed to affect the intrinsic value, the trading intensity and the noise. The proposed model encompasses many important existing models.
We derive the filtering equations to characterize the likelihoods, the posterior, the likelihood ratios and the Bayes factors of the proposed model. We further study the Bayesian inference (estimation and model selection) via filtering. Especially, we employ the Markov chain approximation method to construct easily-parallelizable, recursive efficient algorithms to compute the posteriors and others, and we prove the convergence of such algorithms. The general theory is applied to a specific model built for UHF Treasury notes data from GovPX. The consistency of Bayes estimators for the specific model is proven. We find that the buyer-seller initiation dummy and the economic news dummy in volatility are statistically significant, which has important implications in financial market microstructure theory.