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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A test for the absence of aliasing or white noise in locally stationary wavelet time series. / Eckley, Idris Arthur; Nason, Guy P. .
In: Biometrika, Vol. 105, No. 4, 24.09.2018, p. 833–848.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Eckley, IA & Nason, GP 2018, 'A test for the absence of aliasing or white noise in locally stationary wavelet time series', Biometrika, vol. 105, no. 4, pp. 833–848. https://doi.org/10.1093/biomet/asy040

APA

Eckley, I. A., & Nason, G. P. (2018). A test for the absence of aliasing or white noise in locally stationary wavelet time series. Biometrika, 105(4), 833–848. https://doi.org/10.1093/biomet/asy040

Vancouver

Eckley IA, Nason GP. A test for the absence of aliasing or white noise in locally stationary wavelet time series. Biometrika. 2018 Sept 24;105(4):833–848. doi: 10.1093/biomet/asy040

Author

Eckley, Idris Arthur ; Nason, Guy P. . / A test for the absence of aliasing or white noise in locally stationary wavelet time series. In: Biometrika. 2018 ; Vol. 105, No. 4. pp. 833–848.

Bibtex

@article{19b0c2c212a94e36832fa12c22298284,
title = "A test for the absence of aliasing or white noise in locally stationary wavelet time series",
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. ",
author = "Eckley, {Idris Arthur} and Nason, {Guy P.}",
year = "2018",
month = sep,
day = "24",
doi = "10.1093/biomet/asy040",
language = "English",
volume = "105",
pages = "833–848",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "4",

}

RIS

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 -