Table 4: Granger causality test results of the third part of the frameworks.

Null hypothesis 𝐹 -statisticProbabilityResult

ENERGY does not Granger cause ΔIM3.011850.0525Rejected*
ΔIM does not Granger cause ENERGY0.905540.4067Accepted
ENERGY does not Granger cause EX4.671600.0109Rejected**
EX does not Granger cause ENERGY0.872600.4202Accepted
ENERGY does not Granger cause EX_I4.556790.0121Rejected**
EX_I does not Granger cause ENERGY0.927580.3980Accepted
ENERGY does not Granger cause EX_HI4.249860.0162Rejected**
EX_HI does not Granger cause ENERGY1.484000.2304Accepted
ENERGY does not Granger cause ΔEX_NHI1.669730.1766Accepted
ΔEX_NHI does not Granger cause ENERGY0.385450.7637Accepted
OIL does not Granger cause ΔIM3.614860.0295Rejected**
ΔIM does not Granger cause OIL0.214090.8075Accepted
OIL does not Granger cause EX9.135760.0002Rejected***
EX does not Granger cause OIL1.314520.2720Accepted
OIL does not Granger cause EX_I9.111790.0002Rejected***
EX_I does not Granger cause OIL1.420010.2452Accepted
OIL does not Granger cause EX_HI8.401030.0004Rejected***
EX_HI does not Granger cause OIL2.074480.1296Accepted
OIL does not Granger cause ΔEX_NHI4.450120.0052Rejected***
ΔEX_NHI does not Granger cause OIL1.265680.2888Accepted
COAL does not Granger cause ΔIM1.490410.2289Accepted
ΔIM does not Granger cause COAL7.774200.0006Rejected***
COAL does not Granger cause EX1.302780.2762Accepted
EX does not Granger cause COAL7.486130.0001Rejected***
COAL does not Granger cause EX_I1.297810.2779Accepted
EX_I does not Granger cause COAL7.67668<0.001Rejected***
COAL does not Granger cause EX_HI2.287150.1054Accepted
EX_HI does not Granger cause COAL9.023000.0002Rejected***
COAL does not Granger cause ΔEX_NHI0.983300.4028Accepted
ΔEX_NHI does not Granger cause COAL3.381810.0202Rejected**
GAS does not Granger cause ΔIM2.327560.1014Accepted
ΔIM does not Granger cause GAS1.337120.2660Accepted
GAS does not Granger cause EX2.175860.1174Accepted
EX does not Granger cause GAS4.705850.0106Rejected**
GAS does not Granger cause EX_I2.121370.1238Accepted
EX_I does not Granger cause GAS4.735000.0103Rejected**
GAS does not Granger cause EX_HI2.376970.0966Rejected*
EX_HI does not Granger cause GAS4.417510.0138Rejected**
GAS does not Granger cause ΔEX_NHI4.233760.0068Rejected***
ΔEX_NHI does not Granger cause GAS4.397570.0055Rejected***

Note: (1) ***, **, and *represent significance at the 1%, 5%, and 10% levels, respectively.
(2) Δ denotes the nonstationary series variable after first-order differences.