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Activity Number:
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393
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Type:
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Invited
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Date/Time:
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Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #300151 |
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Title:
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Wavelet Processes and Adaptive Estimation of Sparse Evolutionary Wavelet Spectra
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Author(s):
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Sebastien van Bellegem*+ and Rainer von Sachs
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Companies:
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Université Catholique de Louvain and Université Catholique de Louvain
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Address:
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Institut de Statistique, Louvain-La-Neuve, B1348, Belgium
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Keywords:
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time series ; wavelets ; pointwise estimation ; adaptive smoothing ; local stationarity
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Abstract:
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Inference for time series is often based on the assumption of covariance stationarity. However, many time series in the applied sciences show a time-varying second-order structure. To model this nonstationarity, R. Dahlhaus proposed a concept of "local stationarity" which attempts to model and estimate the time variation of the second-order quantities. We introduce a wavelet-based model of local stationarity. 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. One particularly interesting subcase arises when this representation is sparse, meaning that the nonstationary autocovariance process may be decomposed in the autocorrelation wavelets basis using few coefficients. We present a new test of sparsity for the wavelet spectrum. It is based on a nonasymptotic result on the deviations of a functional periodogram. We also present an other application of this result given by the pointwise adaptive estimation of the wavelet spectrum.
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