Table 4.
Comparison of theoretical and empirical values of E(γ | Z(j:k)) and E(Z(j:k))under ARMA-induced dependence.
| i ⇒ | 1 | 25 | 50 | 1 | 25 | 50 | 1 | 25 | 50 | 1 | 25 | 50 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
| ||||||||||||
| k ⇓ | Simulated E(γ) | Analytical E(γ) | Simulated E(Z) | Analytical E(Z) | ||||||||
|
| ||||||||||||
| 1K | 0.63 | 0.10 | 0.07 | 0.73 | 0.10 | 0.07 | 3.15 | 1.91 | 1.62 | 3.51 | 2.03 | 1.70 |
| 5K | 1.46 | 0.24 | 0.16 | 1.59 | 0.23 | 0.16 | 4.03 | 2.64 | 2.39 | 4.15 | 2.69 | 2.41 |
| 10K | 1.89 | 0.33 | 0.23 | 2.06 | 0.33 | 0.23 | 4.37 | 2.90 | 2.65 | 4.44 | 2.95 | 2.68 |
| 100K | 3.21 | 1.09 | 0.77 | 3.29 | 1.09 | 0.76 | 5.45 | 3.80 | 3.5 | 5.45 | 3.81 | 3.54 |
| 5M | 4.17 | 3.36 | 3.07 | 4.19 | 3.36 | 3.07 | 6.95 | 5.53 | 5.21 | 6.96 | 5.53 | 5.22 |