Selecting and combining models with self-organizing maps for long-term forecasting of chaotic time series

When time series are generated by chaotic systems, a reasonable estimation of large prediction horizons is hard to obtain, but this may be required by some applications. Over the last years, some researchers have focused on the use of ensembles and meta-learning as a strategy for improving prediction accuracy. This paper addresses the problem of selecting and combining models for the design of efficient long-term predictors of chaotic time series based on meta-learning and self-organization. We propose and evaluate the use of four heuristic rules for selecting models using a self-organizing map (SOM) neural network and meta-features. The meta-features are extracted from the performances of each involved model when applied to the training time series. A trained SOM map, which was generated using these meta-features, allows the selection of models with diverse behaviors. Two strategies for the combination of models are compared; one is based on the average and a second is based on the median of the forecasts of the selected models. The experiments were executed using four types of series: the time series dataset provided by the NN5 tournament and time series generated from the Mackey-Glass equation, from an ARIMA model and from a sine function. In most cases, the best results were obtained using a percentage of the models belonging to the group that contained the best model. Our results also showed that a combination using a median strategy obtained better results that using an average strategy.