Hawkes Processes with Delayed Granger Causality
Chao Yang Hengyuan Miao Shuang Li
We aim to explicitly model the delayed Granger causal effects based on
multivariate Hawkes processes. The idea is inspired by the fact that a causal
event usually takes some time to exert an effect. Studying this time lag itself
is of interest. Given the proposed model, we first prove the identifiability of
the delay parameter under mild conditions. We further investigate a model
estimation method under a complex setting, where we want to infer the posterior
distribution of the time lags and understand how this distribution varies
across different scenarios. We treat the time lags as latent variables and
formulate a Variational Auto-Encoder (VAE) algorithm to approximate the
posterior distribution of the time lags. By explicitly modeling the time lags
in Hawkes processes, we add flexibility to the model. The inferred time-lag
posterior distributions are of scientific meaning and help trace the original
causal time that supports the root cause analysis. We empirically evaluate our
model's event prediction and time-lag inference accuracy on synthetic and real
data, achieving promising results.