Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum

By Guy Nason, R. von Sachs, G. Kroisandt. 2000

399 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Economics and Econometrics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/84fdf10c2207df17f149ce1ad6ec90afdc2dce31

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Citations in the corpus

Cross wavelet analysis: significance testing and pitfalls (2004, neutral): “This measure is called wavelet periodogram ( Nason et al. , 2000) to emphasize that it is like the Fourier periodogramχ2-distributed with 2 degrees of freedom and thus not a consistent estimator. This does not contradict the finding ofPercival and Walden(2000), who state that the global wavelet spec”
Multiple‐change‐point detection for high dimensional time series via sparsified binary segmentation (2015, methodology): “i=−∞ S (j) i (z)Ψi(τ) (from Nason et al. (2000)), c(z, τ) = −1 ∑”
Using wavelets for time series forecasting: Does it pay off? (2010, background): “…of Ψ we use the local autocovariance fuction c(z, τ) = ∞∑ m=1 WSm(z)Ψm(τ), Ψm(τ) = ∑ n∈N Ψm,n(0)Ψm,n(τ), z ∈ (0, 1] , τ ∈ Z, which is based on the unique wavelet spectrum WSm(z),m ∈ N, z ∈ (0, 1] and converges against the autocovariance function of the process itself (see Nason et al., 2000).”
A review of change point detection methods (2018, background): “org/package= wbsts Change in 2nd order stationary structure [105] BinSeg [52, 83]”
Editorial: Special issue on time series analysis in the biological sciences (2012, methodology): “…have been proposed, the locally stationary Fourier-based model of Priestley (1965) and Dahlhaus (1997), the locally stationary wavelets model in Nason et al. (2000), the SLEX (smooth localized Fourier) model in Ombao et al. (2005), and a local spline approach taken in Rosen et al. (2009).”
Testing temporal constancy of the spectral structure of a time series (2009, background): “Mallat et al. (1998) considered adaptive covariance estimators of locally stationary processes, while Nason et al. (2000) considered processes where the time-varying spectral representation and the associated Fourier basis have been replaced by a representation with respect to a wavelet basis.”
A Haar-Fisz technique for locally stationary volatility estimation (2006, methodology): “Locally stationary linear models (Dahlhaus, 1997; Nason et al., 2000) seem to be a particularly interesting option here, as they combine linearity with a modelling approach whereby the time-varying parameters are modelled as “well-behaved” functions defined on a compact interval, which enables a…”