Graphical models and causality for multivariate time series

(joint work with Michael Eichler)

Different concepts based on graphical models are presented in order to discuss causality relations between the components of multivariate time series.

One concept is based on the partial spectral coherence of two components given the remaining components of the series leading to an undirected graph. Another concept is based on the notion of Granger causality leading to directed graphs. We present results on the relation between Markov properties of the processes and path properties of the graph.

Inference for time series graphs is done by parametric and nonparametric methods in combination with model selection or testing procedures. We discuss inference with AR-models, the partial spectral coherence and a partial correlation function. As an example we consider multivariate autoregressive processes.

The methods are applied to air pollution data, EEG data and spike trains from a network of neurons.