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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A test for the absence of aliasing or white noise in locally stationary wavelet time series
AU - Eckley, Idris Arthur
AU - Nason, Guy P.
PY - 2018/9/24
Y1 - 2018/9/24
N2 - 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.
AB - 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.
U2 - 10.1093/biomet/asy040
DO - 10.1093/biomet/asy040
M3 - Journal article
VL - 105
SP - 833
EP - 848
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 4
ER -