A Systems View Across Time and Space
Hypotheses → / test criteria↓ | Null hypothesis: no cointegration | Statistic (prob.) | Weighted statistic (prob.) | |
---|---|---|---|---|
No deterministic trend | Alternative hypothesis: common AR coefficients (within-dimension) | Panel v-statistic | 0.183 (0.42) | − 1.05 (0.83) |
Panel rho-statistic | 0.21 (0.51) | 1.16 (0.87) | ||
Panel PP-statistic | − 0.72 (0.23) | 0.36 (0.64) | ||
Panel ADF-statistic | − 0.97 (0.16) | 0.16 (0.56) | ||
Alternative hypothesis: individual AR coefficients (between-dimension) | Group rho-statistic | 2.189 (0.93) | - | |
Group PP-statistic | 0.65 (0.74) | - | ||
Group ADF-statistic | 0.32 (0.62) | - | ||
Deterministic intercept and trend | Alternative hypothesis: common AR coefficients (within-dimension) | Panel v-statistic | 1.506 (0.06) | 1.03 (0.15) |
Panel rho-statistic | − 0.81 (0.20) | 1.05 (0.85) | ||
Panel PP-statistic | − 4.90 (0.00) | − 1.09 (0.13) | ||
Panel ADF-statistic | − 1.89 (0.02) | − 0.49 (0.30) | ||
Alternative hypothesis: individual AR coefficients (between-dimension) | Group rho-statistic | 2.12 (0.95) | - | |
Group PP-statistic | − 0.38 (0.35) | - | ||
Group ADF-statistic | − 0.75 (0.22) | - | ||
No deterministic intercept and trend | Alternative hypothesis: common AR coefficients (within-dimension) | Panel v-statistic | − 0.41 (0.66) | − 1.22 (0.88) |
Panel rho-statistic | − 0.60 (0.27) | 0.92 (0.82) | ||
Panel PP-statistic | − 1.64 (0.05) | 0.22 (0.58) | ||
Panel ADF-statistic | − 1.08 (0.13) | 0.78 (0.78) | ||
Alternative hypothesis: individual AR coefficients (between-dimension) | Group rho-statistic | 2.66 (0.99) | - | |
Group PP-statistic | 1.15 (0.87) | - | ||
Group ADF-statistic | 1.71 (0.95) | - |