Nonlinear Prediction Intervals by the Bootstrap Resampling

Abstract

Many nonlinear prediction algorithms have already been proposed to predict complex behavior produced from nonlinear dynamical systems. If we predict behavior produced from such nonlinear dynamical systems, we have to consider nonlinear prediction methods rather than linear prediction methods. In this paper, we discuss a novel nonlinear modeling framework, which combines a conventional local linear prediction algorithm and bootstrap resampling scheme. Then, we showed that the proposed bootstrap nonlinear prediction method is effective by performing numerical simulations. we proposed a new method to evaluate predictability by estimating prediction intervals using a distribution of nonlinear bootstrap predicted points, evaluating the validity of the proposed interval estimation comparing to an ensemble prediction which is one of the conventional interval estimation methods. As a result, we find that the bootstrap prediction interval estimation method is more reasonable to make efficient prediction intervals especially in the case of short term prediction.