  We consider the consistency properties of a regularised estimator for the
simultaneous identification of both changepoints and graphical dependency
structure in multivariate time-series. Traditionally, estimation of Gaussian
Graphical Models (GGM) is performed in an i.i.d setting. More recently, such
models have been extended to allow for changes in the distribution, but only
where changepoints are known a-priori. In this work, we study the Group-Fused
Graphical Lasso (GFGL) which penalises partial-correlations with an L1 penalty
while simultaneously inducing block-wise smoothness over time to detect
multiple changepoints. We present a proof of consistency for the estimator,
both in terms of changepoints, and the structure of the graphical models in
each segment.
