Locally adaptive estimation of evolutionary wavelet spectra
(2008) Annals of Statistics — Vol. 36, n° 4, p. 1879-1924 (2008)
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- Abstract
- We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on scales. We propose a pointwise adaptive estimator of the time-varying spectrum. The behavior of the estimator studied in homogeneous and inhomogeneous regions of the wavelet spectrum.
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Citations
Van Bellegem, S., & von Sachs, R. (2008). Locally adaptive estimation of evolutionary wavelet spectra. Annals of Statistics, 36(4), 1879-1924. https://doi.org/10.1214/07-AOS524 (Original work published 2008)