A test for the absence of aliasing or local white noise in locally stationary wavelet time series

• 成果类型: Article
• 署名作者: Eckley, I. A.; Nason, G. P.
• 署名单位: Lancaster University; University of Bristol
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy040
• 发表日期: 2018
• 页码: 833848
• 关键词: Adaptive Estimation

摘要

Aliasing is often overlooked in time series analysis but can seriously distort the spectrum, the autocovariance and their estimates. We show that dyadic subsampling of a locally stationary wavelet process, which can cause aliasing, results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum. We develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location, and illustrate its application on simulated data and a wind energy time series. A useful by-product is a new test for local white noise. The tests are robust with respect to model misspecification in that the analysis and synthesis wavelets do not need to be identical. Hence, in principle, the tests work irrespective of which wavelet is used to analyse the time series, although in practice there is a trade-off between increasing statistical power and time localization of the test.