Improvements on Scalable Stochastic Bayesian Inference Methods for Multivariate Hawkes Process

TL;DR

This paper evaluates and improves scalable stochastic Bayesian inference methods for Multivariate Hawkes Processes, introducing a novel likelihood approximation that enhances accuracy while maintaining computational efficiency.

Contribution

It presents a new likelihood approximation for MHPs and compares stochastic inference algorithms, demonstrating improved accuracy and efficiency in simulations and real financial data.

Findings

The new likelihood approximation reduces boundary effect errors.

Stochastic gradient methods achieve high accuracy with lower computational cost.

Application to S&P 500 data reveals insights into sector risk dynamics.

Abstract

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study the risk dynamics in the Standard & Poor's 500 intraday index prices among its 11 sectors.