Graphical Modeling of High-Dimensional Time Series

We consider the problem of inferring the conditional independence graph of a high-dimensional stationary multivariate real-valued Gaussian time series. A p-variate Gaussian time series graphical model associated with an undirected graph with p vertices is defined as the family of time series that obey the conditional independence restrictions implied by the edge set of the graph. We present a novel formulation of joint graphical lasso in frequency domain, suitable for dependent time series, generalizing current time-domain approaches to i.i.d. time series. The approach is nonparametric. First a sufficient statistic set in frequency domain is developed, and then a penalized log-likelihood of the sufficient statistic set is optimized. An optimization algorithm based on alternating minimization is presented and illustrated via numerical examples.