A Hybrid Model for Forecasting Sunspots Time Series Based on Variational Mode Decomposition and Backpropagation Neural Network Improved by Firefly Algorithm

Table 1

Comparison of various methods for error analysis of forecasting samples.

Models	Error indicators
	MAE	RMSE	MAPE
BP	3.4037	3.8647	0.2065
FA-BP	2.1931	3.0317	0.1072
EMD-BP	2.7458	3.1338	0.1596
VMD-BP	1.8497	2.2107	0.0867
VMD-FA-BP	1.2208	1.7117	0.0435