Hawkes processes with hidden marks

Abstract

We develop a novel Hawkes process (HP) model with hidden marks for financial event data, where the hidden marks are used to take account the effect of some extra random errors (ERE) caused by data collection mechanisms and some data cleaning procedures. We further propose a Bayesian method for parameter estimation. We use simulation studies and two data applications to evaluate the performance of the estimation method and the impact of ERE on the intensity of an underlying financial process and explain how to use the proposed model in practice. Our results show that the proposed estimation method works well, and they also confirm that when ERE cause information about the underlying process to be lost, the intensity function may be underestimated. We further find that the proposed model performs better in the presence of ERE compared with the standard HP model.