Recurrent error-based ridge polynomial neural networks for time series forecasting - Hassan Saeed, Waddah Waheeb (2019)
Time series forecasting has attracted much attention due to its impact on many practical applications. Neural networks (NNs) have been attracting widespread interest as a promising tool for time series forecasting. The majority of NNs employ only autoregressive (AR) inputs (i.e., lagged time series values) when forecasting time series. Moving-average (MA) inputs (i.e., errors) however have not adequately considered. The use of MA inputs, which can be done by feeding back forecasting errors as extra network inputs, alongside AR inputs help to produce more accurate forecasts. Among numerous existing NNs architectures, higher order neural networks (HONNs), which have a single layer of learnable weights, were considered in this research work as they have demonstrated an ability to deal with time series forecasting and have an simple architecture. Based on two HONNs models, namely the feedforward ridge polynomial neural network (RPNN) and the recurrent dynamic ridge polynomial neural network (DRPNN), two recurrent error-based models were proposed. These models were called the ridge polynomial neural network with error feedback (RPNN-EF) and the ridge polynomial neural network with error-output feedbacks (RPNN-EOF). Extensive simulations covering ten time series were performed. Besides RPNN and DRPNN, a pi-sigma neural network and a Jordan pi-sigma neural network were used for comparison. Simulation results showed that introducing error feedback to the models lead to significant forecasting performance improvements. Furthermore, it was found that the proposed models outperformed many state-of-the-art models. It was concluded that the proposed models have the capability to efficiently forecast time series and that practitioners could benefit from using these forecasting models.