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

Chapitre 4. Multivariate portmanteau test for weak structural VARMA models 147
Table 4.12 – 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)-(4.15).
Model Length n Level Standard Test Modified Test
m = 1 m = 2 m = 1 m = 2
α = 1% 20.5 11.0 2.7 0.8
II 500 α = 5% 40.9 26.0 6.6 3.1
α = 10% 54.5 35.9 10.4 7.4
α = 1% 21.3 13.7 2.4 1.4
II 1,000 α = 5% 40.1 26.4 6.8 4.5
α = 10% 52.9 37.1 11.5 8.1
α = 1% 23.6 15.9 2.5 1.4
II 2,000 α = 5% 42.6 29.9 7.4 5.4
α = 10% 53.8 38.6 11.9 9.6
II : Weak VARMA(1,1) model (4.13)-(4.15) with θ0 = (0,0,0)
Model Length n Level Standard Test Modified Test
m = 3 m = 4 m = 3 m = 4
α = 1% 9.2 4.8 0.8 0.2
II 500 α = 5% 22.3 11.7 2.4 1.3
α = 10% 32.2 17.0 5.7 3.0
α = 1% 12.5 12.1 0.8 1.2
II 1,000 α = 5% 24.7 22.6 4.2 4.7
α = 10% 33.4 31.1 8.4 8.4
α = 1% 13.7 13.1 0.9 0.9
II 2,000 α = 5% 28.9 26.5 3.2 4.0
α = 10% 39.2 36.6 7.4 8.5
II : Weak VARMA(1,1) model (4.13)-(4.15) with θ0 = (0,0,0)
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