Abstract

We build a multidimensional point process with Hawkes intensities that depend on some state representation modeled as a hidden Markov chain. Estimation of the process intensities and state transition probabilities is carried out using an expectation-maximization algorithm. An alternative supervise machine learning approach is also provided for this task. We provide in-depth numerical and computational analysis of the performances of the estimation algorithms. The results extend and improve previous modeling propositions developped in more restricted frameworks (with e.g. restricted excitation kernels). We use the model to analyse equity and cryptocurrency market data and show that it is an efficient tool to retrieve financially interpretable market states described by different intensity regimes.