Paper: arXiv 2609.27614

Authors: Bram Wouters, Cees Diks

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated framework for noise reduction, offering a novel approach to optimal linear denoising in high-dimensional time series. It demonstrates strong empirical rigor through simulations and real-world applications, with code availability enhancing reproducibility. The overall contribution is significant for quantitative finance.

Research Flowchart

  flowchart TD
    A[Research Goal: Model-Agnostic Noise Reduction for High-Dimensional Time Series] --> B{Key Methodology: Latent Dynamic Component & Optimal Projection};
    B --> C{Inputs: High-Dimensional Time Series Data (e.g., Stock Returns, Macroeconomic Indicators)};
    C --> D[Computational Processes: Lagged Covariance Matrices, Bootstrap Dimension Selection, Low-Rank Representation];
    D --> E[Outcomes: Denoised Series, Improved Subspace Estimation, Reduced Reconstruction Error, Enhanced Forecast Accuracy];
    E --> F[Validation: Simulations & Empirical Applications];