Locally Adaptive Estimation of Evolutionary Wavelet Spectra
نویسندگان
چکیده
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. 1. Introduction. The spectral analysis of time series is a large field of great interest from both theoretical and practical viewpoints. The fundamental starting point for this analysis is the Cramér representation, stating that all zero-mean second order stationary processes X t , t ∈ Z, may be written
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