THÈSE Estimation, validation et identification des modèles ARMA ...

Chapitre 4. Multivariate portmanteau test for weak structural VARMA models 151
Table 4.16 – Empirical size (in %) of the standard and modified versions of the LB test in
the case of the strong VARMA(2,2) model (4.18)-(4.14).
Model Length n Level Standard Test Modified Test
m = 1 m = 2 m = 1 m = 2
α = 1% 93.2 91.0 72.2 86.6
I 500 α = 5% 99.4 97.4 93.1 96.2
α = 10% 99.8 98.9 97.8 98.1
α = 1% 100.0 99.9 99.5 99.9
I 1,000 α = 5% 100.0 100.0 100.0 100.0
α = 10% 100.0 100.0 100.0 100.0
α = 1% 100.0 100.0 100.0 100.0
I 2,000 α = 5% 100.0 100.0 100.0 100.0
α = 10% 100.0 100.0 100.0 100.0
I : Strong VARMA(2,2) model (4.18)-(4.14) with θ0 = (4.19)
Model Length n Level Standard Test Modified Test
m = 3 m = 4 m = 3 m = 4
α = 1% 91.8 89.9 89.2 85.7
I 500 α = 5% 97.7 97.4 97.1 96.3
α = 10% 99.3 98.9 98.7 98.3
α = 1% 100.0 100.0 100.0 100.0
I 1,000 α = 5% 100.0 100.0 100.0 100.0
α = 10% 100.0 100.0 100.0 100.0
α = 1% 100.0 100.0 100.0 100.0
I 2,000 α = 5% 100.0 100.0 100.0 100.0
α = 10% 100.0 100.0 100.0 100.0
I : Strong VARMA(1,1) model (4.18)-(4.14) with θ0 = (4.19)