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

Japanese

高次元時間シリーズにおけるノイズ削減のためのモデルアゴニティックデータフレームワークを開発し、観測ホワイトノイズによって汚染された低次元暗号ダイナミックコンポーネントの最適な回復を明示的にターゲットとします。暗号ダイナミクスが低次元の線形ダイナミックサブスペースに生きていると仮定すると、我々はダイナミックサブスペースに最適な線形投影を特徴付け、信号およびノイズスペースの相対的な方向性に関して残留エラーの地理的記述を提供します。我々は、暗号ダイナミックサブスペースおよび遅延コヴァリンスマトリックスに基づいて最適な投影を提案し、ブート

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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