Parameter Selection for Prediction-Based Denoising of Measured Deterministic Time Series

This study focuses on a numerical algorithm for noise reduction in discretely sampled observables from deterministic dynamical systems. The method utilises forecasting within the space formed by time-delay reconstruction, effectively leveraging the system’s inherent dynamics to distinguish signal from noise. A key challenge is the optimal selection of denoising parameters without access to clean data. To address this, we propose a selection strategy that utilises the sample entropy of the filtered signal, reflecting the expectation of reduced randomness and increased determinism in the denoised data. The effectiveness of this approach is tested on complex chaotic observables contaminated with Gaussian white noise.