Model-agnostic noise reduction for high-dimensional time series data
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.
Related
- Factor Model Estimation for High-Dimensional Time Series with Heteroskedastic Noise
- An adaptive L2-type test for high-dimensional white noise
- An Iterative Active Subspace Approach for Model Order Reduction of Parametric Systems with High-Dimensional Parameter Spaces
- On Detecting Multiple Simultaneous Change-points in High Dimensional Non-Stationary Time Series
- High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series
BibTeX
@misc{wouters2026modelagnostic,
title = {{Model-agnostic noise reduction for high-dimensional time series data}},
author = {Bram Wouters and Cees Diks},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27614},
eprint = {2609.27614},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27614},
}
RIS
TY - UNPB
TI - Model-agnostic noise reduction for high-dimensional time series data
AU - Bram Wouters
AU - Cees Diks
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27614
UR - https://arxiv.org/abs/2609.27614
AB - 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.
ER -