Poisson Graphical Granger Causality by Minimum Message Length

Graphical Granger models are popular models for causal inference among time series. In this paper we focus on the Poisson graphical Granger model where the time series follow Poisson distribution. We use minimum message length principle for determination of causal connections in the model. Based on the dispersion coefficient of each time series and on the initial maximum likelihood estimates of the regression coefficients, we propose a minimum message length criterion to select the subset of causally connected time series with each target time series. We propose a genetic-type algorithm to find this set. To our best knowledge, this is the first work on applying the minimum message length principle to the Poisson graphical Granger model. Common graphical Granger models are usually applied in scenarios when the number of time observations is much greater than the number of time series, normally by several orders of magnitude. In the opposite case of "short" time series, these methods often suffer from overestimation. We demonstrate in the experiments with synthetic Poisson and point process time series that our method is for short time series superior in precision to the compared causal inference methods, i.e. the heterogeneous Granger causality method, the Bayesian causal inference method using structural equation models LINGAM and the point process Granger causality.