Newest papers

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

Bram Wouters, Cees G. H. Diks · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.27614 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

我们开发了高维时间序列中噪声减少的模型预测数据框架,明确目标是对被观察白噪音污染的低维隐形动态组件的最佳恢复。假设隐形动态生活在低维线性动态子空间中,我们特征了对动态子空间的最佳线性投影,并在温和的条件下提供了对信号和噪音空间相对方向的残余错误的几何描述。我们提出了动态子空间的估计和基于延迟的形动态子矩阵的最佳投影,启动尺寸选择,以及结构噪音的低级代表。在温和的条件下,结果的否定序列被显示以通常的参数率与其目标人口相匹配。模拟表明,拟议的方法可以显著提高子空间的估计,

Machine translation (Meta M2M100); the English original follows.

Abstract

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.

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Topics: Mathematics, Subspace topology, Estimator, Algorithm, Series (stratigraphy), Projection (relational algebra)

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