Lagged-Covariance Denoising for High-Dimensional Time Series

Summary

This paper develops a model-independent way to recover low-dimensional dynamics from high-dimensional time series corrupted by observational white noise. It assumes the latent process evolves within a low-dimensional linear dynamic subspace and characterizes the linear projection that best recovers that component. The remaining error is described geometrically through the orientation of signal and noise spaces.

The proposed procedure estimates the dynamic subspace and projection from lagged covariance matrices, selects dimension with bootstrap methods, and represents structured noise at low rank. Under stated mild conditions, the denoised series converges to its population target at a parametric rate. Simulations report gains in subspace estimation, reconstruction, and one-step forecasts against orthogonal projection denoising and raw observations. Applications include stock returns and a multivariate macroeconomic series. The abstract does not specify data periods, implementation details, or trading performance, so the reported forecasting improvements do not establish profitability.

Key ideas

• The method targets latent low-dimensional dynamics obscured by observational white noise.
• Lagged covariance matrices provide estimates of the dynamic subspace and its recovery projection.
• Bootstrap dimension selection and low-rank noise representation are part of the estimation procedure.
• The residual reconstruction error depends on the relative orientation of signal and noise spaces.
• Reported simulations and applications assess reconstruction and forecasts, not trading profitability.

Tags

# 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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