Perfect Sampling of Multivariate Hawkes Process

TL;DR

This paper introduces a perfect sampling algorithm for multivariate Hawkes processes that generates unbiased stationary samples efficiently, with explicit complexity analysis and optimization schemes.

Contribution

It presents the first perfect sampling method for multivariate Hawkes processes, including explicit complexity analysis and parameter optimization techniques.

Findings

Algorithm produces i.i.d. stationary samples without bias

Explicit complexity expression provided

Numerical schemes optimize sampling efficiency

Abstract

As an extension of self-exciting Hawkes process, the multivariate Hawkes process models counting processes of different types of random events with mutual excitement. In this paper, we present a perfect sampling algorithm that can generate i.i.d. stationary sample paths of multivariate Hawkes process without any transient bias. In addition, we provide an explicit expression of algorithm complexity in model and algorithm parameters and provide numerical schemes to find the optimal parameter set that minimizes the complexity of the perfect sampling algorithm.