Wavelet Methods for Time Series Analysis

By Michael R. Chernick. Technometrics, 2001

2,033 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/84448eceabe055f28ce3c0d74c4fb8447730485f

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Citations in the corpus

Adaptive reconfiguration of fractal small-world human brain functional networks (2006, methodology): “Wavelet analysis, unlike Fourier analysis, allows both time and frequency localization of a signal; see Percival & Walden (1) for a comprehensive text on time series analysis using wavelets and Bullmore et al.”
Testing the Conventional and Islamic Financial Market Contagion: Evidence from Wavelet Analysis (2016, methodology): “For a more complete and comprehensive development of the theory and use of wavelets, please see Percival and Walden (2000), Gençay, Selçuk, and Whitcher (2002) and Gallegati (2012).”
Measuring Business Cycles: A Wavelet Analysis of Economic Time Series (2008, positive): “The filter relating the wavelet coefficients b̃jk at level j to the original signal has a frequency response Bj(ω) = H1(2 J−j−1ω) J−j−2∏ l=0 H0(2 lω), (10) which is a bandpass filter with an approximate passband |ω| ∈ [π/2J−j, π/2J−j−1] (Percival and Walden, 2000, pp. 96–97).”
Flux calculation of short turbulent events – comparison of three methods (2016, background): “Based on the second derivative of a Gaussian probability density function (Percival and Walden, 2008), the Mexican hat wavelet can be expressed as ψMh (u)≡ 2 · ( 1− u 2 σ 2 ) · e− u2 2σ π 1 4 · √ 3 · σ = 2 π 1 4 · √ 3 · ( 1− u2 ) · e− u2 2 with σ = 1.”
TSclust: An R Package for Time Series Clustering (2014, methodology): “A detailed description of wavelet methods for time series analysis can be seen in Percival and Walden (2006) and some interesting references where wavelets are used to clustering time series are Struzik and Siebes (1999), Chan and Fu (1999), Popivanov and Miller (2002), Chan, Fu, and Yu (2003) and…”
Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human visual cortical areas (2016, neutral): “Per sensor, each data epoch was demeaned, Hann-tapered, zero-padded to 1 s length, and Fourier transformed to give a spectrum between 1 and 140 Hz (Percival and Walden, 2000).”
Review of noise removal techniques in ECG signals (2020, methodology): “The universal hard-thresholding wavelet shrinkage (UHTWS) method [100] applies a hard-thresholding function to the wavelet coefficients when considering the universal threshold.”
On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter (2005, positive): “This type of assumption is typical in the semi-parametric estimation setting (see for instance Robinson (1995) and Moulines and Soulier (2002)).”
Procedures for numerical analysis of circadian rhythms (2007, methodology): “An alternative procedure for handling the nonstationarity of circadian rhythms is the wavelet transform, which was developed specifically to handle non-stationary time series (e.g. Percival & Walden 2000).”
Measuring capital market efficiency: Global and local correlations structure (2012, methodology): “However, we cannot estimate the fractal dimension D this way for a univariate time series and it is needed to use an alternative estimators used for time series – periodogram estimator [14], Genton estimator [23], Hall-Wood estimator [26] and wavelet-based estimator [25, 43].”
Maximal Overlap Wavelet Statistical Analysis With Application to Atmospheric Turbulence (2006, methodology): “The MODWT differs from the DWT in that it is a highly redundant, nonorthogonal transform (Percival and Walden, 2000, p. 159).”
Improved analysis and modelling of soil diffuse reflectance spectra using wavelets (2009, methodology): “Because the pyramid algorithm requires that there are 2m data, where m is some integer, we first padded each data set by symmetrical reflection (Percival & Walden, 2000) to extend it to the nearest integer power of two in length.”
Analyzing information flow in brain networks with nonparametric Granger causality (2008, methodology): “The multitaper spectral and cross-spectral method introduced by Thomson (1982) is known to provide smooth spectral density function estimates (Percival and Walden, 1993; Percival and Walden, 2000; Walden, 2000; Mitra and Pesaran, 1999).”
Modeling Customer Lifetime Value (2006, methodology): “In this connection, we may be able to borrow from wavelet methods (Percival and Walden 2000).”