Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

• 成果类型: Article
• 署名作者: Dette, Holger; Paparoditis, Efstathios
• 署名单位: Ruhr University Bochum; University of Cyprus
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2009.00709.x
• 发表日期: 2009
• 页码: 831-857
• 关键词: models

摘要

We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on an L-2-distance between the non-parametrically estimated individual spectral densities and an overall, 'pooled' spectral density, the latter being obtained by using the whole set of m time series considered. The effects of the dependence between the time series on the power behaviour of the test are investigated. Some simulations are presented and a real life data example is discussed.