  We propose a novel graphical model selection (GMS) scheme for
high-dimensional stationary time series or discrete time process. The method is
based on a natural generalization of the graphical LASSO (gLASSO), introduced
originally for GMS based on i.i.d. samples, and estimates the conditional
independence graph (CIG) of a time series from a finite length observation. The
gLASSO for time series is defined as the solution of an l1-regularized maximum
(approximate) likelihood problem. We solve this optimization problem using the
alternating direction method of multipliers (ADMM). Our approach is
nonparametric as we do not assume a finite dimensional (e.g., an
autoregressive) parametric model for the observed process. Instead, we require
the process to be sufficiently smooth in the spectral domain. For Gaussian
processes, we characterize the performance of our method theoretically by
deriving an upper bound on the probability that our algorithm fails to
correctly identify the CIG. Numerical experiments demonstrate the ability of
our method to recover the correct CIG from a limited amount of samples.
