Predicting Chaotic Time Series

Abstract:

We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we "learn" the induced nonlinear mapping using a local approximation. This allows us to make short-term predictions of the future behaviour of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Bénard convection, and Taylor-Couette flow.