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基于滞后协方差的高维时间序列去噪

文章 arXiv papers · 作者: Bram Wouters et al.
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总结

本文提出一种与模型无关的方法，从受观测白噪声干扰的高维时间序列中恢复低维动态。该方法假设潜在过程在低维线性动态子空间内演变，并刻画最能恢复该成分的线性投影。剩余误差则通过信号空间与噪声空间的相对方向进行几何描述。

所提程序根据滞后协方差矩阵估计动态子空间和投影，使用自助法选择维度，并以低秩形式表示结构化噪声。在文中所述的温和条件下，去噪序列以参数速率收敛至总体目标。模拟结果显示，与正交投影去噪和原始观测相比，该方法在子空间估计、重构和单步预测方面有所改善。应用包括股票收益和多变量宏观经济序列。摘要未说明数据期间、实现细节或交易表现，因此报告的预测改进并不能证明盈利能力。

核心观点

  • 该方法旨在恢复被观测白噪声掩盖的潜在低维动态。
  • 滞后协方差矩阵用于估计动态子空间及其恢复投影。
  • 估计程序包括通过自助法选择维度，并以低秩形式表示噪声。
  • 残余重构误差取决于信号空间与噪声空间的相对方向。
  • 报告的模拟和应用评估了重构与预测，而非交易盈利能力。

标签

统计学股票机器学习回测
全文
# Model-agnostic noise reduction for high-dimensional time series data


# Model-agnostic noise reduction for high-dimensional time series data









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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。