Analysis and forecasting of crude oil price based on the variable selection-LSTM integrated model

Table 3 Forecasting performance

Types	Models	In-sample			Out-of-sample
Types	Models	RMSE	MAPE (%)	DS (%)	RMSE	MAPE (%)	DS (%)
Time series	RW	4.89	4.02	49.42	5.74	5.19	48.84
Time series	ARMA	4.01	3.54	55.81	4.87	4.53	53.49
Without variables selection	MLP	3.49	2.68	65.70	4.62	3.07	62.79
	RBFNN	3.56	2.33	66.28	4.51	2.91	60.47
	GRNN	3.36	2.37	66.86	4.48	2.85	62.79
	Elman	2.93	1.79	69.19	3.61	2.21	67.44
	WNN	2.39	1.61	70.35	3.44	1.78	67.44
	ELM	2.26	1.52	71.51	3.11	1.63	69.77
	LSTM	2.21	1.35	72.67	3.17	1.56	69.77
GLMNET	MLP	3.58	2.17	66.86	4.49	2.82	60.47
	RBFNN	3.36	2.18	69.17	4.29	2.72	65.12
	GRNN	3.13	2.01	68.60	4.23	2.56	67.44
	Elman	2.05	1.38	74.42	3.18	1.99	69.77
	WNN	1.95	1.29	75.58	2.98	1.82	72.09
	ELM	1.83	1.26	77.33	2.93	1.48	69.77
	LSTM	1.88	1.17	78.49	2.76	1.43	74.42
Spike-slab Lasso	MLP	3.02	2.11	66.28	4.12	2.74	65.12
	RBFNN	2.59	1.72	69.77	3.57	2.43	67.44
	GRNN	2.57	1.65	70.35	3.42	2.23	65.12
	Elman	1.74	0.92	76.16	2.89	1.41	72.09
	WNN	1.63	1.02	78.49	2.91	1.45	74.42
	ELM	1.57	0.95	80.23	2.62	1.31	72.09
	LSTM	1.48	0.85	80.81	2.45	1.02	76.74
Bayesian model averaging	MLP	2.81	1.97	70.93	3.92	2.64	67.44
	RBFNN	2.25	1.66	75.00	3.41	2.23	72.09
	GRNN	2.05	1.52	74.42	3.18	2.09	69.77
	Elman	1.28	0.95	78.49	2.43	1.01	76.74
	WNN	1.21	0.92	82.56	2.08	1.05	74.42
	ELM	1.29	0.78	83.72	2.13	0.91	76.74
	LSTM	1.12	0.74	84.88	2.04	0.83	81.40

Note: The table reports the RMSE values of each model forecast, while the PT statistics are in the parenthesis. ** denotes a rejection of the null hypothesis at the 1% significance level