From: Portmanteau test statistics for seasonal serial correlation in time series models
Model | \(\phi _{1}\) | \(\phi _{2}\) | \(\theta _{1}\) | \(\theta _{2}\) | \(\Phi _{1}\) | \(\Phi _{2}\) | \(\Theta _{1}\) | \(\Theta _{2}\) | \(\hat{Q}_{m}(4)\) | \(\tilde{Q}_{m}(4)\) | \(\mathfrak {D}_{m}(4)\) | \(\hat{Q}_{m}(12)\) | \(\tilde{Q}_{m}(12)\) | \(\mathfrak {D}_{m}(12)\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Fitted by SAR (1) | ||||||||||||||
1 | * | * | * | * | * | * | −0.5 | * | 0.111 | 0.133 | 0.129 | 0.100 | 0.113 | 0.119 |
2 | * | * | * | * | * | * | −0.6 | 0.3 | 0.333 | 0.301 | 0.389 | 0.301 | 0.301 | 0.356 |
3 | * | * | * | * | 0.7 | * | −0.4 | * | 0.087 | 0.091 | 0.063 | 0.084 | 0.090 | 0.062 |
4 | * | * | * | * | 0.1 | 0.3 | * | * | 0.102 | 0.119 | 0.120 | 0.092 | 0.095 | 0.089 |
5 | 0.3 | * | * | * | −0.35 | * | * | * | 0.786 | 0.663 | 0.652 | 0.763 | 0.641 | 0.661 |
6 | 0.4 | * | * | * | * | * | −0.8 | * | 0.961 | 0.998 | 0.971 | 0.951 | 0.996 | 0.965 |
7 | * | * | * | * | 0.4 | −0.6 | 0.3 | * | 0.371 | 0.401 | 0.442 | 0.363 | 0.396 | 0.406 |
8 | 0.7 | 0.2 | * | * | −0.5 | * | * | * | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
9 | 0.7 | * | 0.7 | * | −0.8 | * | * | * | 0.124 | 0.096 | 0.075 | 0.119 | 0.094 | 0.066 |
10 | 0.1 | 0.3 | * | * | * | * | −0.8 | * | 0.867 | 0.918 | 0.889 | 0.844 | 0.907 | 0.887 |
Fitted by SMA (1) | ||||||||||||||
11 | * | * | * | * | 0.5 | * | * | * | 0.126 | 0.148 | 0.150 | 0.111 | 0.144 | 0.143 |
12 | * | * | * | * | * | * | −0.6 | 0.3 | 0.175 | 0.172 | 0.264 | 0.161 | 0.165 | 0.244 |
13 | * | * | * | * | 0.7 | * | −0.4 | * | 0.382 | 0.701 | 0.665 | 0.378 | 0.700 | 0.662 |
14 | * | * | * | * | 0.1 | 0.3 | * | * | 0.113 | 0.100 | 0.211 | 0.109 | 0.098 | 0.203 |
15 | 0.3 | * | * | * | −0.35 | * | * | * | 0.760 | 0.689 | 0.662 | 0.755 | 0.679 | 0.654 |
16 | 0.4 | * | * | * | * | * | −0.8 | * | 0.958 | 0.961 | 0.913 | 0.953 | 0.958 | 0.908 |
17 | * | * | * | * | 0.4 | * | 0.3 | * | 0.204 | 0.367 | 0.265 | 0.201 | 0.295 | 0.257 |
18 | 0.7 | 0.2 | * | * | −0.5 | * | * | * | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
19 | 0.7 | * | 0.7 | * | −0.8 | * | * | * | 0.632 | 0.761 | 0.935 | 0.628 | 0.757 | 0.931 |
20 | 0.1 | 0.3 | * | * | * | * | −0.8 | * | 0.779 | 0.705 | 0.700 | 0.770 | 0.698 | 0.698 |