Cointegration tests of ICE Brent Crude Futures contracts
| Panel A: daily futures prices | |||||
| ICE Brent Crude Futures prices: 1-month vs 2-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0324 | 40.7115 | 19.99 | |
| 1 | 1 | 0.0046 | 5.0373 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest. E-value | df | χ2 | Pr>χ2 |
| 0 | 0.0324 | 0.0324 | 2 | 0.30 | 0.8608 |
| 1 | 0.0044 | 0.0046 | 1 | 0.28 | 0.5950 |
| ICE Brent Crude Futures prices: 1-month vs 3-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0251 | 32.569 | 19.99 | |
| 1 | 1 | 0.0047 | 5.1139 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest E-value | df | χ2 | Pr>χ2 |
| 0 | 0.025 | 0.0251 | 2 | 0.31 | 0.8557 |
| 1 | 0.0044 | 0.0047 | 1 | 0.3 | 0.5833 |
| ICE Brent Crude Futures prices: 2-month vs 3-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0198 | 26.7586 | 19.99 | |
| 1 | 1 | 0.0047 | 5.1174 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest. E-value | df | χ2 | Pr>χ2 |
| 0 | 0.0198 | 0.0198 | 2 | 0.37 | 0.8325 |
| 1 | 0.0198 | 0.0198 | 2 | 0.37 | 0.8325 |
| Panel B: 30-minute intraday futures prices | |||||
| ICE Brent Crude Futures prices: 1-month vs 2-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0024 | 101.728 | 19.99 | |
| 1 | 1 | 0.0001 | 5.4757 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest. E-value | df | χ2 | Pr>χ2 |
| 0 | 0.0024 | 0.0024 | 2 | 0.32 | 0.8529 |
| 1 | 0.0001 | 0.0001 | 1 | 0.31 | 0.5807 |
| ICE Brent Crude Futures prices: 1-month vs 3-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0016 | 58.5668 | 19.99 | |
| 1 | 1 | 0.0002 | 5.7255 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest. E-value | df | χ2 | Pr>χ2 |
| 0 | 0.0016 | 0.0016 | 2 | 0.32 | 0.854 |
| 1 | 0.0002 | 0.0002 | 1 | 0.29 | 0.5873 |
| ICE Brent Crude Futures prices: 2-month vs 3-months | |||||
| H0: rank=r | H1: rank>r | Eigenvalue | Trace | 5% crit. val. | |
| 0 | 0 | 0.0026 | 91.751 | 19.99 | |
| 1 | 1 | 0.0002 | 5.855 | 9.13 | |
| Hypothesis test of the H0: restriction | |||||
| Rank | E-value | Rest. E-value | df | χ2 | Pr>χ2 |
| 0 | 0.0026 | 0.0026 | 2 | 0.32 | 0.854 |
| 1 | 0.0002 | 0.0002 | 1 | 0.31 | 0.5781 |
| ICE Brent Crude Futures prices: 1-month vs 2-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0324 | 40.7115 | 19.99 | |
| 1 | 1 | 0.0046 | 5.0373 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest. E-value | df | Pr> | |
| 0 | 0.0324 | 0.0324 | 2 | 0.30 | 0.8608 |
| 1 | 0.0044 | 0.0046 | 1 | 0.28 | 0.5950 |
| ICE Brent Crude Futures prices: 1-month vs 3-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0251 | 32.569 | 19.99 | |
| 1 | 1 | 0.0047 | 5.1139 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest E-value | df | Pr> | |
| 0 | 0.025 | 0.0251 | 2 | 0.31 | 0.8557 |
| 1 | 0.0044 | 0.0047 | 1 | 0.3 | 0.5833 |
| ICE Brent Crude Futures prices: 2-month vs 3-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0198 | 26.7586 | 19.99 | |
| 1 | 1 | 0.0047 | 5.1174 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest. E-value | df | Pr> | |
| 0 | 0.0198 | 0.0198 | 2 | 0.37 | 0.8325 |
| 1 | 0.0198 | 0.0198 | 2 | 0.37 | 0.8325 |
| ICE Brent Crude Futures prices: 1-month vs 2-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0024 | 101.728 | 19.99 | |
| 1 | 1 | 0.0001 | 5.4757 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest. E-value | df | Pr> | |
| 0 | 0.0024 | 0.0024 | 2 | 0.32 | 0.8529 |
| 1 | 0.0001 | 0.0001 | 1 | 0.31 | 0.5807 |
| ICE Brent Crude Futures prices: 1-month vs 3-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0016 | 58.5668 | 19.99 | |
| 1 | 1 | 0.0002 | 5.7255 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest. E-value | df | Pr> | |
| 0 | 0.0016 | 0.0016 | 2 | 0.32 | 0.854 |
| 1 | 0.0002 | 0.0002 | 1 | 0.29 | 0.5873 |
| ICE Brent Crude Futures prices: 2-month vs 3-months | |||||
| Eigenvalue | Trace | 5% crit. val. | |||
| 0 | 0 | 0.0026 | 91.751 | 19.99 | |
| 1 | 1 | 0.0002 | 5.855 | 9.13 | |
| Hypothesis test of the | |||||
| Rank | E-value | Rest. E-value | df | Pr> | |
| 0 | 0.0026 | 0.0026 | 2 | 0.32 | 0.854 |
| 1 | 0.0002 | 0.0002 | 1 | 0.31 | 0.5781 |
Notes: Cointegration test results are presented in the table. Panel A presents the results for daily data and Panel B presents the results for the 30-minute intraday frequency data
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