Observing and Predicting Chaotic Signals: Is 2% Noise Too Much?

We discuss the influence of noise on the analysis of complex time series data. How harmful it is depends on the nature of the noise, the complexity of the signal and on the application in mind. We will give generally valid upper bounds on the feasible noise level for dimension, entropy and Lyapunov estimates and lower bounds for the optimal achievable prediction error. We illustrate in a number of examples why it is hard to reach these bounds in practice. We briefly sketch methods to detect, analyze and reduce measurement noise.

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