Properties of Direct Multi-Step Ahead Prediction of Chaotic Time Series and Out-of-Bag Estimate for Model Selection

This paper examines properties of direct multi-step ahead (DMS) prediction of chaotic time series and out-of-bag (OOB) estimate of the prediction performance for model selection. Although previous studies of DMS estimation suggest that the DMS technique allows us accuracy improvements from iterated one-step ahead (IOS) prediction. However, it has not considered chaotic time series which has long-term unpredictability as well as short-term predictability, where the boundary of the horizon of long-term and short-term is not known previously. As a result of the model selection, the CAN2 with a large number of units are selected, which is supposed to be useful for avoiding unpredictable data of chaotic time series. We examine the relationship between the OOB prediction and the prediction for the test data, and we suggest that there is a mixed distribution of very small and very big magnitude of prediction errros owing to chaotic time series. We show the effectiveness and the properties of the present method by means of numerical experiments.