On sparse high-dimensional graphical model learning for dependent time series

We consider the problem of inferring conditional independence graph (CIG) a sparse, high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain formulation based on sufficient statistic for observed series is presented. investigate an alternating direction method multipliers (ADMM) approach optimization lasso penalized log-likelihood. provide conditions convergence in Frobenius norm inverse PSD estimators to true value, jointly across all frequencies, where number frequencies are allowed increase with sample size. This result also yields rate convergence. empirically selection tuning parameters Bayesian information criterion, and illustrate our using numerical examples utilizing both synthetic real data.