Table 3 The result of ARDL co-integration

Bounds testing to co-integration

Optimal lag

F-statistics

X ² normal

X ² ARCH

X ² reset

X ² serial

F_CO2(CO₂/FUE, GDP, POP, REN

4, 2, 2, 1

14.2739

1.1704

[1] 0.5462

[1] 0.0150

[2] 1.8323

F_FUE(FUE/CO₂, GDP, POP, REN

4,1, 2, 1

30.7047

0.2829

[1] 0.7610

[1] 1.2294

[2] 3.9920

F_GDP(GDP/CO₂, FUE, POP, REN

2, 2, 1, 1

6.7908

1.1704

[1] 0.0150

[1] 1.1809

[2] 5.5904

F_POP(POP/CO₂, FUE, GDP, REN

2, 1, 2, 1

14.4282

0.5437

[1] 0.1968

[1] 2.1207

[2] 2.7049

F_REN(REN/CO₂, FUE, GDP, POP

2, 1, 1, 1

5.0009

1.8256

[1] 0.2633

[1] 1.9967

[2] 1.8149

Significance level (%)

Lower bounds (0)

Upper bounds (1)

 1

3.43

4.60

 5

2.86

3.99

 10

2.57

3.66