Panel A: Bounds test for cointegration
Linear ARDL (Symmetric) Model for WTI
Null: No long run relationship
Linear ARDL (Symmetric) Model for BRENT
Test Statistic Value k Test Statistic Value k
F-statistic 65.65 2 F-statistic 71.40 2
Pesaran et al. (2001) Critical value bounds Pesaran et al. (2001) Critical value bounds
Significance I(0) I(1) Significance I(0) I(1)
1% 6.34 7.52 1% 6.34 7.52
5% 4.87 5.85 5% 4.87 5.85
10% 4.19 5.06 10% 4.19 5.06
Narayan (2004) Critical value bounds Narayan (2004) Critical value bounds
Significance I(0) I(1) Significance I(0) I(1)
1% 3.42 7.84 1% 3.42 7.84
5% 2.23 5.43 5% 2.23 5.43
10% 1.74 4.46 10% 1.74 4.46
Nonlinear ARDL (Asymmetric) Model for WTI
Null: No long run relationship
Nonlinear ARDL (Asymmetric) Model for BRENT
Test Statistic Value K Test Statistic Value K
F-statistic 51.24 3 F-statistic 54.75 3
Pesaran et al. (2001) Critical value bounds Pesaran et al. (2001) Critical value bounds
Significance I(0) I(1) Significance I(0) I(1)
1% 5.17 6.36 1% 5.17 6.36
5% 4.01 5.07 5% 4.01 5.07
10% 3.47 4.45 10% 3.47 4.45
Narayan (2004) Critical value bounds Narayan (2004) Critical value bounds
Significance I(0) I(1) Significance I(0) I(1)
1% 3.30 7.01 1% 3.30 7.01
5% 2.20 4.96 5% 2.20 4.96
10% 1.75 4.14 10% 1.75 4.14
Panel B: The BDS test results for nonlinearity
Variables SSR BRENT WTI GFI
Dimension BDS Statistic BDS Statistic BDS Statistic BDS Statistic
2 0.008 (0.175) 0.188 (0.000)* -4.23E-05 (0.9446) 0.168 (0.000)*
3 0.022 (0.019)** 0.319 (0.000)* -0.0001 (0.9250) 0.285 (0.000)*
4 0.029 (0.010)* 0.408 (0.000)* -0.0003 (0.9096) 0.361 (0.000)*
5 0.032 (0.006)** 0.467 (0.000)* -0.0004 (0.8962) 0.410 (0.000)*
6 0.033 (0.004)* 0.506 (0.000)* -0.0006 (0.8841) 0.439 (0.000)*