Bayesian estimation of the spectral density of a time series

• 成果类型: Article
• 署名作者: Choudhuri, N; Ghosal, S; Roy, A
• 署名单位: University System of Ohio; Case Western Reserve University; North Carolina State University; University System of Maryland; University of Maryland Baltimore County
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000000557
• 发表日期: 2004
• 页码: 1050-1059
• 关键词: posterior consistency; inference; mixtures

摘要

This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain Monte Carlo algorithm for sampling front this posterior distribution is described that is used for computing the posterior mean, variance, and other statistics. A consistency result is established for this pseudoposterior distribution that holds for a short-memory Gaussian time series and under some conditions on the prior. To prove this asymptotic result, a general consistency theorem of Schwartz is extended for a triangular array of independent, nonidentically distributed observations. This extension is also of independent interest. A simulation study is conducted to compare the proposed method with some existing methods. The method is illustrated with the well-studied sunspot dataset.