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

Eckley, Idris Arthur and Nason, Guy P. (2018) A test for the absence of aliasing or white noise in locally stationary wavelet time series. Biometrika, 105 (4). 833–848. ISSN 0006-3444

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Abstract

Aliasing is often overlooked in time series analysis but can seriously distort the spectrum, 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 it 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 to model misspecification in that it is unnecessary for the analysis and synthesis wavelets to be identical. Hence, in principle, the tests work irrespective of which wavelet is used to analyze the time series, though in practice there is a tradeoff between increasing statistical power and time localization of the test.

Item Type:
Journal Article
Journal or Publication Title:
Biometrika
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1100/1101
Subjects:
ID Code:
125641
Deposited By:
Deposited On:
31 May 2018 13:44
Refereed?:
Yes
Published?:
Published
Last Modified:
08 Apr 2020 04:25