Energy Demand Forecasting: Combining Cointegration Analysis and Artificial Intelligence Algorithm

Table 2

Results based on Ng-Perron unit root test.

Variables	Level				The first difference				The second difference
	MZa	MZt	MSB	MPT	MZa	MZt	MSB	MPT	MZa	MZt	MSB	MPT
E		−1.71	0.23	4.02		−2.90	0.15	1.93		−0.93	0.44	10.62
X1	1.19	1.74	1.46	145.21		−3.10	0.15	1.45	−1.94	−0.97	0.50	12.46
X2		−2.45	0.18	2.39		−2.17	0.22	2.70		−2.50	0.19	2.08
X3		0.41	0.55	24.74		−2.56	0.18	2.03		−2.40	0.20	2.17
X4	−4.68	−1.30	0.28	5.66		−1.81	0.27	3.74		−2.61	0.18	1.85
X5	−2.23	−0.88	0.39	9.69		−2.38	0.18	2.52		−3.30	0.15	1.16
E	−2.17	−0.97	0.44	37.97	−7.99	−1.79	0.23	11.90	−5.41	−1.62	0.30	16.77
X1	−3.16	−1.07	0..34	24.85	−0.41	−0.25	0.61	85.70	−9.73	−2.21	0.23	9.36
X2		−4.25	0.12	2.70	−10.23	−2.19	0.21	9.20	−13.39	−2.58	0.19	6.85
X3		−2.87	0.17	5.57	−13.87	−2.58	0.19	6.87	−11.60	−2.39	0.21	7.96
X4	−13.31	−2.57	0.19	6.91	−6.75	−1.82	0.27	13.50	−13.89	−2.62	0.19	6.64
X5	−0.48	−0.20	0.41	42.25	−14.15	−2.60	0.18	6.83		−3.34	0.15	4.08
	Critical values (intercept)							Critical values (intercept and trend)
1% level	−13.80	−2.58	0.17	1.78				−23.80	−3.42	0.14	4.03
5% level	−8.10	−1.98	0.23	3.17				−17.30	2.91	0.17	5.48
10% level	−5.70	−1.62	0.27	4.45				−14.20	−2.62	0.18	6.67

Note. , , and ∗∗∗ denote significance at the 10%, 5%, and 1% levels, respectively; , and denote the ln form of electricity demand, population, GDP, economic structure, urbanization, and energy price, respectively.