Biometrika Advance Access originally published online on February 28, 2007
Biometrika 2007 94(2):335-345; doi:10.1093/biomet/asm022
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Copyright © 2007 Biometrika Trust
Articles |
Automatic estimation of multivariate spectra via smoothing splines
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968, U.S.A.
Department of Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
ori{at}math.utep.edu
stoffer{at}pitt.edu
Received for publication 1 August 2005.
Revision received 1 August 2006.
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Abstract |
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The classical method for estimating the spectral density of a multivariate time series is first to calculate the periodogram, and then to smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have different degrees of smoothness. We propose a Bayesian approach that uses Markov chain Monte Carlo techniques to fit smoothing splines to each component, real and imaginary, of the Cholesky decomposition of the periodogram matrix. The spectral estimator is then obtained by reconstructing the spectral estimator from the smoothed Cholesky decomposition components. Our technique produces an automatically smoothed spectral matrix estimator along with samples from the posterior distributions of the parameters to facilitate inference.
Key Words: coherency • Cholesky decomposition • DNA nucleotide sequence • Markov chain Monte Carlo • multivariate spectral density • smoothing spline • spectral analysis • spectral envelope