New predication of chaotic time series based on local Lyapunov exponent

A new method of predicting chaotic time series is presented based on local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula using the definition of local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision than two older methods. Effects of number of referential state vectors and added noise on forecasting accuracy are also studied numerically.