Inference for High-Dimensional Sparse Spectral Precision Matrices

Statistical inference for the spectral precision matrix at a given frequency allows us to assess frequency-specific conditional relationships among the components of a stationary multivariate time series. We construct a debiased complex graphical lasso estimator at any fixed frequency by leveraging the full likelihood structure of neighboring discrete Fourier transforms. An application to real fMRI data further reveals distinct patterns of functional connectivity across selected frequencies.