Estimating Dynamic Graphical Models from Multivariate Time-Series Data: Recent Methods and Results

Dynamic graphical models aim to describe the time-varying dependency structure of multiple time-series. In this article we review research focusing on the formulation and estimation of such models. The bulk of work in graphical structurelearning problems has focused in the stationary i.i.d setting, we present a brief overview of this work before introducing some dynamic extensions. In particular we focuson two classes of dynamic graphical model; continuous (smooth) models which are estimated via localised kernels, and piecewise models utilising regularisation based estimation. We give an overview of theoretical and empirical results regarding these models, before demonstrating their qualitative difference in the context of a real-world financial time-series dataset. We conclude with a discussion of the state of the field and future research directions.