发表机构
University of Amsterdam（阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种模型无关的高维时间序列降噪框架，通过估计低维动态子空间和最优投影，以参数速率收敛，并在模拟和实证中显著提升子空间估计、重建及预测精度。
AI 中文摘要
我们开发了一个模型无关的框架，用于降低高维时间序列中的噪声，该框架明确针对从观测白噪声污染中最佳恢复低维潜在动态成分。在潜在动态存在于低维线性动态子空间的假设下，我们刻画了到动态子空间的最优线性投影，并从信号与噪声空间的相对方向角度提供了残差的几何描述。我们基于滞后协方差矩阵、自助法维度选择以及结构化噪声的低秩表示，提出了动态子空间和最优投影的估计器。在温和条件下，所得到的去噪序列被证明以通常的参数速率收敛到其总体目标。模拟显示，与基于正交投影的去噪和原始数据相比，所提出的方法能显著改善子空间估计、重建误差和一步超前预测精度。该方法通过高维股票收益和包含20个变量的宏观经济指标时间序列的实证应用加以说明。
英文摘要
We develop a model-agnostic framework for noise reduction in high-dimensional time series that explicitly targets optimal recovery of a low-dimensional latent dynamic component contaminated by observational white noise. Under the assumption that the latent dynamics live in a low-dimensional linear dynamic subspace, we characterize the optimal linear projection onto the dynamic subspace and provide a geometric description of the residual error in terms of the relative orientation of the signal and noise spaces. We propose estimators for the dynamic subspace and the optimal projection based on lagged covariance matrices, bootstrap dimension selection, and a low-rank representation of the structured noise. Under mild conditions, the resulting denoised series is shown to converge to its population target at the usual parametric rate. Simulations show that the proposed method can substantially improve subspace estimation, reconstruction error, and one-step-ahead forecast accuracy compared with both orthogonal projection-based denoising and the raw data. The approach is illustrated by empirical applications to high-dimensional stock returns and to a 20-variate time series of macroeconomic indicators.
Comments36 pages; working paper
