Contiguity of the Whittle measure for a Gaussian 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: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/91.1.211
• 发表日期: 2004
• 页码: 211218
• 关键词: SPECTRAL DENSITY; parameter-estimation; Periodogram; regression; likelihood

摘要

For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators. In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of estimators and test statistics derived under the Whittle measure can be carried over to the actual distribution.