A shrinkage estimator for spectral densities

Abstract

We propose a shrinkage estimator for spectral densities based on a multilevel normal hierarchical model. The first level captures the sampling variability via a likelihood constructed using the asymptotic properties of the periodogram. At the second level, the spectral density is shrunk towards a parametric time series model. To avoid selecting a particular parametric model for the second level, a third level is added which induces an estimator that averages over a class of parsimonious time series models. The estimator derived from this model, the model averaged shrinkage estimator, is consistent, is shown to be highly competitive with other spectral density estimators via simulations, and is computationally inexpensive.