Locally adaptive estimation of evolutionary wavelet spectra

• 成果类型: Article
• 署名作者: Van Bellegem, Sebastien; von Sachs, Rainer
• 署名单位: Universite Catholique Louvain
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS524
• 发表日期: 2008
• 页码: 1879-1924
• 关键词: time-series analysis; stationary-processes; models

摘要

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.