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Activity Number: 109 - Time Series and Forecasting
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 8:30 AM to 10:20 AM
Sponsor: Business and Economic Statistics Section
Abstract #330879
Title: Regularized Estimation of High-Dimensional Spectral Density
Author(s): Sumanta Basu*
Companies: Cornell University
Keywords: Multivariate Spectral Density; Thresholding; Regularization; Sparsity

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).

Authors who are presenting talks have a * after their name.

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