Abstract
Recently, we have presented a method of probabilistic prediction of chaotic time series. The method employs learning machines involving strong learners capable of making predictions with desirably long predictable horizons, where, however, usual ensemble mean for making representative prediction is not effective when there are predictions with shorter predictable horizons. Thus, the method selects a representative prediction from the predictions generated by a number of learning machines involving strong learners as follows: first, it obtains plausible predictions holding large similarity of attractors with the training time series and then selects the representative prediction with the largest predictable horizon estimated via LOOCV (leave-one-out cross-validation). The method is also capable of providing average and/or safe estimation of predictable horizon of the representative prediction. We have used CAN2s (competitive associative nets) for learning piecewise linear approximation of nonlinear function as strong learners in our previous study, and this paper employs bagging (bootstrap aggregating) to improve the performance, which enables us to analyze the validity and the effectiveness of the method.
Highlights
A number of methods for time series prediction have been studied, and our methods have awarded 3rd and 2nd places in the competitions of time series prediction held at IJCNN’04 [3] and ESTSP’07 [4], respectively
The method selects a representative prediction from the predictions generated by a number of learning machines involving strong learners as follows: first, it obtains plausible predictions holding large similarity of attractors with the training time series and selects the representative prediction with the largest predictable horizon estimated via LOOCV
Instead of using model selection methods employing the estimation of the MSE, we have developed a method of probabilistic prediction of chaotic time series [7]
Summary
A number of methods for time series prediction have been studied (cf. [1, 2]), and our methods have awarded 3rd and 2nd places in the competitions of time series prediction held at IJCNN’04 [3] and ESTSP’07 [4], respectively. Most of the methods shown in [8] use ensemble mean for representative forecast, our method in [7] (see below for details) uses an individual prediction selected from a set of plausible predictions for the representative because our method employs learning machines involving strong learners capable of making predictions with small error for a desirably long duration and we can see that ensemble mean does not work when the set of predictions for the ensemble involves a prediction with short predictable horizon This is owing mainly to the exponential increase in prediction error of chaotic time series after the predictable horizon
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