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Biometrika 2006 93(1):179-195; doi:10.1093/biomet/93.1.179
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© 2006 Biometrika Trust

A shrinkage estimator for spectral densities

Carsten H. Botts1 and Michael J. Daniels2

1 Department of Mathematics and Statistics, Williams College, Williamstown, Massachusetts 01267, U.S.A. cbotts{at}williams.edu, 2 Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A. mdaniels{at}stat.ufl.edu

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.

Key Words: Bayesian inference; Hierarchical model; Laplace method; Model averaging; Smoothing

Received September 2004. Revised September 2005.


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