Abstract:
This article gives an overview on nonparametric modelling of nonstationary time series and estimation of their time-changing spectral content by modern denoising (smoothing) methods. For the modelling aspect localized decompositions such as various local Fourier (spectral) representations are discussed, among which wavelet and local cosine bases are most prominent ones. For the estimation of the possibly time-varying coefficients of these local representations wavelet denoising algorithms are applied and their particular properties in the context of time--frequency and time--scale analysis is discussed. In particular non--linear wavelet thresholding, including recent developments of generalizing its usefulness for non--identically, correlated and even non--stationary noise, is briefly reviewed as this is the unifying component of the estimation algorithms. The introduced procedures are illustrated by application to various simulated and real data examples from time--frequency and time--scale analysis, respectively.
Citations
|
1190
|
Orthonomal bases of compactly supported wavelets
– Daubechies
- 1988
|
|
371
|
Entropy-based algorithms for best-basis selection
– Coiffman, Wickerhauser
- 1992
|
|
155
|
Translation-invariant de-noising
– Coifman, Donoho
|
|
133
|
Wavelet threshold estimators for data with correlated noise
– Silverman
- 1997
|
|
98
|
Wavelet shrinkage: asymptopia? (with discussion
– Donoho, Johnstone, et al.
- 1995
|
|
89
|
The stationary wavelet transform and some statistical applications
– Nason, Silverman
- 1995
|
|
58
|
Fitting Time Series Models to Nonstationary Processes
– Dahlhaus
- 1997
|
|
42
|
Denoising via soft-thresholding
– Donoho
- 1995
|
|
42
|
Adaptive covariance estimation of locally stationary processes
– Mallat, Papanicolaou, et al.
- 1998
|
|
40
|
Wigner-Ville spectral analysis of nonstationary processes
– Martin, Flandrin
- 1985
|
|
25
|
Spectral density estimation via nonlinear wavelet methods for stationary non-Gaussian time series
– Neumann
- 1996
|
|
23
|
Wavelet estimation of spectral densities in time series analysis
– Gao
- 1993
|
|
20
|
Wavelets, spectrum analysis and 1=f processes
– Abry, Goncalves, et al.
- 1995
|
|
15
|
Remarques sur l’analyze de Fourier à fenêtre
– Coifman, Meyer
- 1991
|
|
13
|
Wavelet thresholding: beyond the Gaussian I.I.D. situation
– Neumann, Sachs
- 1995
|
|
12
|
Estimating covariances of locally stationary processes: rates of convergence of best basis methods
– Donoho, Mallat, et al.
- 1998
|
|
11
|
Asymptotic statistical inference for nonstationary processes with evolutionary spectra
– Dahlhaus
- 1996
|
|
10
|
Nonlinear wavelet estimation of time-varying autoregressive processes
– Dahlhaus, Neumann, et al.
- 1999
|
|
10
|
Wavelet analysis for stationary processes
– Morettin, Chang
- 1995
|
|
9
|
Time-dependent Spectral Analysis of Nonstationary Time Series
– Adak
- 1998
|
|
8
|
Generalized evolutionary spectral analysis and the Weyl spectrum of nonstationary random processes
– Matz, Hlawatsch, et al.
- 1997
|
|
