Semiparametric estimation for multivariate Hawkes processes using dependent Dirichlet processes: An application to order flow data in financial markets

The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand interplay and price formation. In this work, we propose a semiparametric multivariate Hawkes process model that relies on (mixtures of) dependent Dirichlet processes to analyze order flow data. Such a formulation avoids the kind of strong parametric assumptions about the excitation functions of the Hawkes process that often accompany traditional models and which, as we show, are not justified in the case of order flow data. It also allows us to borrow information across dimensions, improving estimation of the individual excitation functions. To fit the model, we develop two algorithms, one using Markov chain Monte Carlo methods and one using a stochastic variational approximation. In the context of simulation studies, we show that our model outperforms benchmark methods in terms of lower estimation error for both algorithms. In the context of real order flow data, we show that our model can capture features of the excitation functions such as non-monotonicity that cannot be accommodated by standard parametric models.