Fig 1.
Ridge Polynomial Neural Network.
PSNN stands for Pi-Sigma Neural Network.
Fig 2.
Dynamic Ridge Polynomial Neural Network.
PSNN stands for Pi-Sigma Neural Network and Z−1 denotes the time delay operator.
Fig 3.
Ridge Polynomial Neural Network with Error Feedback.
PSNN stands for Pi-Sigma Neural Network, d(t + 1) is the desired output at time t + 1 and Z−1 denotes the time delay operator.
Table 1.
Time series information.
Fig 4.
Star brightness time series.
Fig 5.
Monthly smoothed sunspot numbers time series from November 1834 to June 2001.
Fig 6.
Daily Euro/Dollar exchange rate time series from January 3, 2005 to December 31, 2007.
Fig 7.
Mackey–Glass time-delay differential equation time series.
Table 2.
Network topology and training.
Table 3.
Root Mean Squared Error (RMSE) improvement of RPNN-EF to RPNN and DRPNN.
Table 4.
Normalized Mean Squared Error (NMSE) improvement of RPNN-EF to RPNN and DRPNN.
Table 5.
Mean Absolute Error (MAE) improvement of RPNN-EF to RPNN and DRPNN.
Table 6.
Signal to Noise Ratio (SNR) improvement of RPNN-EF to RPNN and DRPNN.
Fig 8.
Network order for the best average simulations on the used time series.
Table 7.
Best Single Simulation Results.
Fig 9.
Correlation function between forecast and observed values for StarBrightness time series based on the best RPNN-EF simulation.
Fig 10.
Correlation function between forecast and observed values for Sunspot time series based on the best RPNN-EF simulation.
Fig 11.
Correlation function between forecast and observed values for EUR/USD time series based on the best RPNN-EF simulation.
Fig 12.
Correlation function between forecast and observed values for Mackey–Glass time series based on the best RPNN-EF simulation.
Fig 13.
Out-of-sample forecasting for StarBrightness time series based on the best RPNN-EF simulation.
Fig 14.
Out-of-sample forecasting for Sunspot time series based on the best RPNN-EF simulation.
Fig 15.
Out-of-sample forecasting for EUR/USD time series based on the best RPNN-EF simulation.
Fig 16.
Out-of-sample forecasting for Mackey–Glass time series based on the best RPNN-EF simulation.
Fig 17.
The histogram of the forecasting error for StarBrightness time series based on the best RPNN-EF simulation.
Fig 18.
The histogram of the forecasting error for Sunspot time series based on the best RPNN-EF simulation.
Fig 19.
The histogram of the forecasting error for EUR/USD time series based on the best RPNN-EF simulation.
Fig 20.
The histogram of the forecasting error for Mackey–Glass time series based on the best RPNN-EF simulation.
Table 8.
Comparison of the performance of various existing models on Sunspot series.
Table 9.
Comparison of the performance of various existing models on Mackey–Glass series.
Fig 21.
Learning curves for StarBrightness time series forecasting based on the best RPNN-EF simulation.
Fig 22.
Learning curves for Sunspot time series forecasting based on the best RPNN-EF simulation.
Fig 23.
Learning curves for Daily Euro/Dollar (EUR/USD) exchange rate time series forecasting based on the best RPNN-EF simulation.
Fig 24.
Learning curves for Mackey–Glass time series forecasting based on the best RPNN-EF simulation.