|
Abstract:
|
Multivariate spectral density estimation is a canonical problem in time series and signal processing with applications in diverse scientific fields including economics, neuroscience and environmental sciences. In this work, we develop a non-asymptotic theory for regularized estimation of high-dimensional spectral density matrices of linear processes using thresholded versions of averaged periodograms. Our results ensure that consistent estimation of spectral density is possible under high-dimensional regime logp = o(n) as long as the true spectral density is weakly sparse. These results complement and improve upon existing results for shrinkage based estimates of spectral density, which require no assumption on sparsity but only ensure consistent estimation in a regime p^2 = o(n).
|
