Graphical Models for Multivariate Time Series

Graphical Models give a graph representation of relations between random variables and processes and they are an important tool for analyzing multivariate data. In this thesis we give a brief introduction to the concept of Graphical Models in static case and then we extend this concept for multivariate data to multivariate time series. We show that conditional independence of components can be represented on a graph where the components are nodes and the lack of arc between two nodes signifies conditional independence. We also present problem to fit an AR model to such a process and show how AR models can be approximated by a low order ARMA model and the benefits of this approximation