TABLE 3.
Some hypothesis tests of time-homogeneous models through likelihood ratios
| LRT | H0vs. H1 | Asymptotic distributiona |
LRTS | P |
|---|---|---|---|---|
| 1 | EU1 vs. EU2 | 0.5χ02 + 0.5χ12 | 0.084 | 0.39 |
| 2 | EU1 vs. EU2* | Simulatedb | 1.060 | 0.16 |
| 3 | EL1 vs. EL2 | 0.5χ02 + 0.5χ12 | 4.92 | 0.013 |
| 4 | PL1 vs. PL2 | 0.5χ02 + 0.5χ12 | 2.54 | 0.055 |
| 5 | EU1 vs. EC1 | χ12 | 275.62 | ≪0.01 |
| 6 | EU1 vs. EL1 | χ22 | 363.91 | ≪0.01 |
| 7 | EC1 vs. EL1 | χ12 | 88.27 | ≪0.01 |
| 8 | EU1 vs. PU1 | χ12 | 179.75 | ≪0.01 |
| 9 | EC1 vs. PC1 | χ12 | 0.022 | 0.88 |
| 10 | EL1 vs. PL1 | χ12 | 17.84 | ≪0.01 |
a
The expected asymptotic behavior of the likelihood-ratio test statistic (LRTS) under H0, with Ω = 40.
b
Simulated finite sample distribution (Figure 6A).