标题： 数据自适应的时间变化谱密度估计 显示英文标题

标题： Data-adaptive estimation of time-varying spectral densities

摘要： 本文介绍了一种针对非平稳时间序列的时间变异性谱密度估计的数据自适应非参数方法。 通常情况下，时间变异性谱密度通过局部核平滑来估计。然而，这些非参数估计器的性能在很大程度上取决于需要在时间和频率方向上指定的平滑带宽。作为传统带宽选择方法的一种替代和扩展，我们提出了一种迭代算法，用于数据自适应地构造局部平滑核。 受传播-分离（Polzehl 和 Spokoiny 2006）概念的启发，该方法的核心思想是在时频平面上的一个点确定一个最大的局部邻域，在此邻域内平滑由数据合理化。通过非参数形状调整平滑核，我们的方法不仅避免了严格意义上的带宽选择问题，还变得更加灵活。它不仅能适应平滑变化光谱中的曲率变化，还能调整时变光谱中的结构突变。 显示英文摘要

摘要： This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The performance of these nonparametric estimators, however, depends crucially on the smoothing bandwidths that need to be specified in both time and frequency direction. As an alternative and extension to traditional bandwidth selection methods, we propose an iterative algorithm for constructing localized smoothing kernels data-adaptively. The main idea, inspired by the concept of propagation-separation (Polzehl and Spokoiny 2006), is to determine for a point in the time-frequency plane the largest local vicinity over which smoothing is justified by the data. By shaping the smoothing kernels nonparametrically, our method not only avoids the problem of bandwidth selection in the strict sense but also becomes more flexible. It not only adapts to changing curvature in smoothly varying spectra but also adjusts for structural breaks in the time-varying spectrum.