A hybrid adaptive time-delay neural network model for multi-step-ahead prediction of sunspot activity

The availability of accurate empirical models for multi-step-ahead (MS) prediction is desirable in many areas. Some ANN technologies, such as multiple-neural network, time-delay neural network (TDNN), and adaptive time-delay neural network (ATNN), have proven successful in addressing various complicated problems. The purpose of this study was to investigate the applicability of neural network MS predictive models. Motivated by the above-mentioned technologies, we proposed a hybrid neural network model, which integrated characteristics decomposition units, and a dynamic spline interpolation unit into the multiple ATNNs. Inside the net, the regular and certain information were extracted to ATNN, while both time delays and weights were dynamically adapted. The yearly average of the sunspots, which has been considered by geophysicists, environment scientists, and climatologists as a complicated non-linear system, was selected to test the hybrid model. Comparative results were presented between a traditional MS predictive model based on TDNN and the proposed model. Validation studies indicated that the proposed model is quite effective in MS prediction, especially for single-factor time series.