Oil spot vs Oil futures: lead-lag relationships
| Panel A: R(1-m Brent Futures)t=R(1-m Brent Futures)t−1+R(BI)t+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(1-m BF)t−1 | t-stat | R(BI)t | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (1) | 0.00002802 | 1.69 | −0.12055 | −3.69 | 1.13313 | 92.1 | −0.006 | −0.2 | 84.7% | MA(1) | 4.19 | 0.522 |
| R(BI)t=R(1-m BF)t+R(1-m BF)t−1+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(1-m BF)t | t-stat | R(1-m BF)t−1 | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (2) | −0.0000201 | −1.38 | 0.78328 | 92.07 | 0.16819 | 6.34 | 0.032 | 1.180 | 85.5% | MA(1) | 3.57 | 0.613 |
| R(2-m BF)t=R(2-m BF)t−1+R(BI)t+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(2-m BF)t−1 | t-stat | R(BI)t | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (3) | 0.00001983 | 0.68 | −0.07091 | −1.96 | 1.07465 | 81.3 | −0.025 | −0.7 | 82.9% | MA(1) | 8.29 | 0.141 |
| Panel B: R(BI)t=R(2-m BF)t+R(2-m BF)t−1+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(2-m BF)t | t-stat | R(2-m BF)t−1 | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (4) | −9.84E-06 | −0.33 | 0.79943 | 81.13 | 0.15156 | 5.0 | 0.044 | 1.4 | 83.8% | MA(1) | 7.66 | 0.176 |
| R(3-m BF)t=R(3-m BF)t−1+R(BI)t+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(3-m BF)t−1 | t-stat | R(BI)t | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (5) | −0.00003 | −0.35 | −0.32448 | −5.66 | 1.03859 | 68.7 | 0.240 | 4.2 | 81.0% | ARMA(1,1) | 7.13 | 0.129 |
| R(BI)t=R(3-m BF)t+R(3-m BF)t−1+R(BI)t−1 | ||||||||||||
| Model | Intercept | t-stat | R(3-m BF)t | t-stat | R(3-m BF)t−1 | t-stat | R(BI)t−1 | t-stat | R2 | EM | χ2(6) | p(χ2) |
| (6) | 0.000057 | 0.7 | 0.78653 | 68.61 | 0.29173 | 6.52 | −0.124 | −2.43 | 81.7% | ARMA(1, 1) | 4.70 | 0.32 |
| Model | Intercept | EM | χ2(6) | |||||||||
| (1) | 0.00002802 | 1.69 | −0.12055 | −3.69 | 1.13313 | 92.1 | −0.006 | −0.2 | 84.7% | MA(1) | 4.19 | 0.522 |
| Model | Intercept | EM | χ2(6) | |||||||||
| (2) | −0.0000201 | −1.38 | 0.78328 | 92.07 | 0.16819 | 6.34 | 0.032 | 1.180 | 85.5% | MA(1) | 3.57 | 0.613 |
| Model | Intercept | EM | χ2(6) | |||||||||
| (3) | 0.00001983 | 0.68 | −0.07091 | −1.96 | 1.07465 | 81.3 | −0.025 | −0.7 | 82.9% | MA(1) | 8.29 | 0.141 |
| Panel B: | ||||||||||||
| Model | Intercept | EM | χ2(6) | |||||||||
| (4) | −9.84E-06 | −0.33 | 0.79943 | 81.13 | 0.15156 | 5.0 | 0.044 | 1.4 | 83.8% | MA(1) | 7.66 | 0.176 |
| Model | Intercept | EM | χ2(6) | |||||||||
| (5) | −0.00003 | −0.35 | −0.32448 | −5.66 | 1.03859 | 68.7 | 0.240 | 4.2 | 81.0% | ARMA(1,1) | 7.13 | 0.129 |
| Model | Intercept | EM | χ2(6) | |||||||||
| (6) | 0.000057 | 0.7 | 0.78653 | 68.61 | 0.29173 | 6.52 | −0.124 | −2.43 | 81.7% | ARMA(1, 1) | 4.70 | 0.32 |
Notes: Lead-lag regression results with Brent Index (BI) and ICE Brent Futures (BF) daily returns are reported in the table. R2 excludes the explanatory power of the error models (EM). χ2 statistic tests for the autocorrelation of residuals for the first six lags. p(χ2) indicates the p-value or the significance level of the χ2 statistic
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