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

Chapitre 4. Multivariate portmanteau test for weak structural VARMA models 148
Table 4.13 – Empirical size (in %) of the standard and modified versions of the LB test in
the case of the weak VARMA(1,1) model (4.13)-(4.16).
Model Length n Level Standard Test Modified Test
m = 1 m = 2 m = 1 m = 2
α = 1% 53.0 46.9 0.1 1.0
III 5,00 α = 5% 71.8 62.9 2.4 4.0
α = 10% 79.6 70.7 6.5 7.4
α = 1% 54.3 47.4 0.1 1.0
III 1,000 α = 5% 72.3 64.7 2.4 3.3
α = 10% 80.4 72.5 6.5 6.9
α = 1% 53.7 48.3 1.0 0.3
III 2,000 α = 5% 72.2 64.8 4.1 3.2
α = 10% 79.5 73.0 10.3 7.6
III : Weak VARMA(1,1) model (4.13)-(4.16) with θ0 = (0.225,−0.313,0.750)
Model Length n Level Standard Test Modified Test
m = 3 m = 4 m = 3 m = 4
α = 1% 36.5 31.4 0.5 0.5
III 500 α = 5% 54.7 48.4 2.6 2.6
α = 10% 63.9 57.4 5.6 5.4
α = 1% 38.8 34.8 0.4 0.3
III 1,000 α = 5% 54.2 50.7 2.7 1.4
α = 10% 64.3 59.5 5.7 3.4
α = 1% 40.0 35.1 0.1 0.1
III 2,000 α = 5% 58.5 51.0 2.4 1.7
α = 10% 66.5 60.9 6.5 5.2
III : Weak VARMA(1,1) model (4.13)-(4.16) with θ0 = (0.225,−0.313,0.750)
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