B0869
Title: Spectral analysis using multitaper Whittle methods with a Lasso penalty
Authors: Peter Craigmile - Hunter College, CUNY (United States) [presenting]
Shuhan Tang - The Ohio State University (United States)
Yunzhang Zhu - Ohio State University (United States)
Abstract: Spectral estimation provides key insights into the frequency domain characteristics of a time series. Naive nonparametric estimates of the spectral density, such as the periodogram, are inconsistent, and the more advanced lag window or multitaper estimators are often still too noisy. An L1 penalized quasi-likelihood Whittle framework is proposed based on multitaper spectral estimates which perform semiparametric spectral estimation for regularly sampled univariate stationary time series. The new approach circumvents the problematic Gaussianity assumption required by least square approaches and achieves sparsity for a wide variety of basis functions. An alternating direction method of multipliers (ADMM) algorithm is presented to efficiently solve the optimization problem and universal threshold and generalized information criterion (GIC) strategies are developed for efficient tuning parameter selection that outperforms cross-validation methods. Theoretically, a fast convergence rate for the proposed spectral estimator is established. The utility of the methodology is demonstrated on simulated series and on the spectral analysis of electroencephalogram (EEG) data.
