Changepoint detection on a graph of time series

Abstract

When analysing multiple time series that may be subject to changepoints, it is sometimes possible to specify a priori, by means of a graph G, which pairs of time series are likely to be impacted by simultaneous changepoints. This article proposes a novel Bayesian changepoint model for multiple time series that borrows strength across clusters of connected time series in G to detect weak signals for synchronous changepoints. The graphical changepoint model is further extended to allow dependence between nearby but not necessarily synchronous changepoints across neighbour time series in G. A novel reversible jump MCMC algorithm making use of auxiliary variables is proposed to sample from the graphical changepoint model. The merit of the proposed model is demonstrated via a changepoint analysis of real network authentication data from Los Alamos National Laboratory (LANL), with some success at detecting weak signals for network intrusions across users that are linked by network connectivity, whilst limiting the number of false alerts.Comment: 31 pages, 13 figure