Automatic estimation of multivariate spectra via smoothing splines

• 成果类型: Article
• 署名作者: Rosen, Ori; Stoffer, David S.
• 署名单位: University of Texas System; University of Texas El Paso; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm022
• 发表日期: 2007
• 页码: 335345
• 关键词: Covariance matrices; models

摘要

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.