Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Length

TL;DR

This paper introduces a novel method for inferring Granger causal relations in multivariate Hawkes processes using the minimum message length principle, which outperforms existing methods especially in short data scenarios.

Contribution

The paper proposes an MML-based optimization and model selection approach for Granger causal inference in MHPs with exponential kernels, reducing overfitting and improving accuracy.

Findings

Achieves high F1 scores in sparse graph settings

Outperforms lasso-based methods in short data scenarios

Identifies causal links consistent with expert knowledge in bond data

Abstract

Multivariate Hawkes processes (MHPs) are versatile probabilistic tools used to model various real-life phenomena: earthquakes, operations on stock markets, neuronal activity, virus propagation and many others. In this paper, we focus on MHPs with exponential decay kernels and estimate connectivity graphs, which represent the Granger causal relations between their components. We approach this inference problem by proposing an optimization criterion and model selection algorithm based on the minimum message length (MML) principle. MML compares Granger causal models using the Occam's razor principle in the following way: even when models have a comparable goodness-of-fit to the observed data, the one generating the most concise explanation of the data is preferred. While most of the state-of-art methods using lasso-type penalization tend to overfitting in scenarios with short time horizons, the proposed MML-based method achieves high F1 scores in these settings. We conduct a numerical study comparing the proposed algorithm to other related classical and state-of-art methods, where we achieve the highest F1 scores in specific sparse graph settings. We illustrate the proposed method also on G7 sovereign bond data and obtain causal connections, which are in agreement with the expert knowledge available in the literature.