演化谱的估计及其在平稳性检验中的应用
Estimation of the Evolutionary Spectra with Application to Stationarity Test
摘要：
在这项工作中，我们提出了一个新的推理程序理解非平稳过程，进化谱的框架下开发的Priestley。在各种非平稳过程的建模框架中，演化谱的显著特点是它关注频率的物理意义。演化谱密度的经典估计是基于由短时傅立叶变换和平滑组成的双窗口技术。然而，已知平滑遭受所谓的偏置泄漏问题。通过将汤姆森的multitaper方法，最初是专为平稳过程，我们提出了一个改进的估计的进化谱密度，并分析其偏差/方差/分辨率的权衡。作为新估计的一个应用，我们进一步提出了一个非参数的基于秩的平稳性检验，并提供了各种实验研究。
英文摘要：
In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the distinguishing feature of the evolutionary spectra is its focus on the physical meaning of frequency. The classical estimate of the evolutionary spectral density is based on a double-window technique consisting of a short-time Fourier transform and a smoothing. However, smoothing is known to suffer from the so-called bias leakage problem. By incorporating Thomson's multitaper method that was originally designed for stationary processes, we propose an improved estimate of the evolutionary spectral density, and analyze its bias/variance/resolution tradeoff. As an application of the new estimate, we further propose a non-parametric rank-based stationarity test, and provide various experimental studies.
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