Bootstrap nonlinear prediction.

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy data series. In this paper, we proposed a scheme to effectively use near-neighbor information for more accurate estimation of the Jacobian matrix using the bootstrap resampling method. Then, to confirm the validity of the proposed method, we applied it to a mathematical model and several real time series. As a result, we confirmed that the proposed method greatly improves nonlinear predictability, not only for noise-corrupted mathematical models but also for real time series.