Learning Network of Multivariate Hawkes Processes: A Time Series Approach

TL;DR

This paper introduces a method to learn the causal influence network among multivariate Hawkes processes, enabling the recovery of causal structures in complex time series data with applications in finance and social media analysis.

Contribution

The paper presents a novel algorithm for identifying the support of the excitation matrix in multivariate Hawkes processes, linking it to the Directed Information graph for causal inference.

Findings

Algorithm accurately recovers causal networks in synthetic data.

Effective in real-world datasets like stock markets and MemeTracker.

Establishes equivalence between excitation support and causal influence graph.

Abstract

Learning the influence structure of multiple time series data is of great interest to many disciplines. This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix. We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.