Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis (SSA) and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey–Glass attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.