标题： 时间序列中充分维度降低的傅里叶方法 显示英文标题

标题： Fourier Methods for Sufficient Dimension Reduction in Time Series

摘要： 降维一直是高维数据分析中最重要的和最具挑战性的问题之一。 在时间序列分析的背景下，我们的重点是条件均值和方差函数的估计和推断。 通过使用保留关于响应变量足够信息的中心均值和方差降维子空间，可以有效地估计时间序列的未知均值和方差函数。 虽然文献中提出了几种估计时间序列中心均值和方差子空间（TS-CMS 和 TS-CVS）的方法，但这些方法往往计算量大，难以应用于实际问题。 通过使用傅里叶变换，我们推导出 TS-CMS 和 TS-CVS 的显式估计量。 这些提出的估计量被证明是一致的、渐近正态的且高效的。 进行了模拟研究以评估所提出方法的性能。 结果表明，我们的方法比现有方法显著更准确且计算效率更高。 此外，该方法已应用于加拿大猞猁数据集。 显示英文摘要

摘要： Dimensionality reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean and variance functions. By using central mean and variance dimension reduction subspaces that preserve sufficient information about the response, one can effectively estimate the unknown mean and variance functions of the time series. While the literature presents several approaches to estimate the time series central mean and variance subspaces (TS-CMS and TS-CVS), these methods tend to be computationally intensive and infeasible for practical applications. By employing the Fourier transform, we derive explicit estimators for TS-CMS and TS-CVS. These proposed estimators are demonstrated to be consistent, asymptotically normal, and efficient. Simulation studies have been conducted to evaluate the performance of the proposed method. The results show that our method is significantly more accurate and computationally efficient than existing methods. Furthermore, the method has been applied to the Canadian Lynx dataset.