Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significance testing
Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significance testing
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DOI：
10.1103/physreve.75.016707
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发表时间：
2007-01-01
影响因子：
2.4
通讯作者：
Holschneider, M.
中科院分区：
文献类型：
--
作者：
Maraun, D.;Kurths, J.;Holschneider, M.
提出了一类等价的非平稳高斯随机过程，定义在小波域中。这些过程用小波乘法器来表征，并表现出明确的随时间变化的谱特性。它们允许人们生成任何小波谱的实现。在此框架下，研究了连续小波谱的估计问题，即计算任意估计的连续小波谱的方差和偏置。最后，我们开发了一种连续小波谱的显著性检验方法，克服了多重检验的困难；它利用连续小波变换的基本性质来判断一个逐点显著的结果是过程的真实特征，还是与典型的随机波动难以区分。该试验在敏感性和特异性方面与常规试验进行了比较。介绍了一种连续小波谱分析与合成软件包。
We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.