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Abstract:
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We propose a general nonlinear filtering framework with marked point process observations for financial ultra-high frequency (UHF) data. The proposed model encompasses many important existing models. We derive SPDEs such as 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. We find that the buyer-seller initiation dummy and the economic news dummy in volatility are statistically significant.
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