A wavelet-Fisz approach to spectrum estimation

We propose a new approach to wavelet threshold estimation of spectral densities of stationary time series. Our proposal addresses the problem of heteroscedasticity and non-normality of the (tapered) periodogram. We estimate thresholds for the empirical wavelet coefficients of the periodogram as appropriate linear combinations of the periodogram values similar to empirical scaling coefficients. Our solution introduces 'asymptotically noise-free reconstruction thresholds' which parallels classical wavelet theory for nonparametric regression with independently and identically distributed Gaussian errors. Our simulations show promising results that clearly improve on existing approaches. In addition, we derive theoretical results on the near-optimal rate of convergence of the minimax mean-square risk for a class of spectral densities, including those of low regularity.

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Document type	Article de périodique (Journal article) – Article de recherche
Publication date	2008
Language	Anglais
Journal information	"Journal of Time Series Analysis" - Vol. 29, no. 5, p. 868-880 (2008)
Peer reviewed	yes
Publisher	Blackwell Publishing (Oxford)
issn	0143-9782
e-issn	1467-9892
Publication status	Publié
Affiliation	UCL - EUEN/STAT - Institut de statistique
Keywords	spectral density estimation ; wavelet thresholding ; wavelet-Fisz ; periodogram ; Besov spaces ; smoothing
Links	https://doi.org/10.1111/j.1467-9892.2008.00586.x[DOI] http://hdl.handle.net/2078.1/36426[Handle]

See also
	[boreal:91374]	A wavelet-Fisz approach to spectrum estimation