Probabilistic Prediction of Chaotic Time Series Using Similarity of Attractors and LOOCV Predictable Horizons for Obtaining Plausible Predictions

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This paper presents a method for probabilistic prediction of chaotic time series. So far, we have developed several model selection methods for chaotic time series prediction, but the methods cannot estimate the predictable horizon of predicted time series. Instead of using model selection methods employing the estimation of mean square prediction error (MSE), we present a method to obtain a probabilistic prediction which provides a prediction of time series and the estimation of predictable horizon. The method obtains a set of plausible predictions by means of using the similarity of attractors of training time series and the time series predicted by a number of learning machines with different parameter values, and then obtains a smaller set of more plausible predictions with longer predictable horizons estimated by LOOCV (leave-one-out cross-validation) method. The effectiveness and the properties of the present method are shown by means of analyzing the result of numerical experiments.