THÈSE Estimation, validation et identification des modèles ARMA ...
THÈSE Estimation, validation et identification des modèles ARMA ...
THÈSE Estimation, validation et identification des modèles ARMA ...
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Chapitre 4. Multivariate portmanteau test for weak structural V<strong>ARMA</strong> models 150<br />
Table 4.15 – Empirical size (in %) of the standard and modified versions of the LB test in<br />
the case of the weak V<strong>ARMA</strong>(2,2) model (4.18)-(4.15).<br />
Model Length n Level Standard Test Modified Test<br />
m = 1 m = 2 m = 1 m = 2<br />
α = 1% 91.7 90.7 27.8 40.3<br />
II 500 α = 5% 98.2 97.1 56.0 63.7<br />
α = 10% 99.4 98.5 69.6 74.6<br />
α = 1% 99.8 99.8 62.1 78.2<br />
II 1,000 α = 5% 100.0 99.9 85.0 89.5<br />
α = 10% 100.0 99.9 91.6 93.9<br />
α = 1% 100.0 100.0 91.4 95.0<br />
II 2,000 α = 5% 100.0 100.0 96.7 97.3<br />
α = 10% 100.0 100.0 97.4 97.9<br />
II : Weak V<strong>ARMA</strong>(2,2) model (4.18)-(4.15) with θ0 = (4.19)<br />
Model Length n Level Standard Test Modified Test<br />
m = 3 m = 4 m = 3 m = 4<br />
α = 1% 92.6 90.4 36.2 27.2<br />
II 500 α = 5% 97.5 97.0 59.6 51.0<br />
α = 10% 98.5 98.4 70.7 62.9<br />
α = 1% 99.9 99.7 79.3 75.0<br />
II 1,000 α = 5% 100.0 100.0 91.1 89.3<br />
α = 10% 100.0 100.0 94.5 93.4<br />
α = 1% 100.0 100.0 95.7 96.0<br />
II 2,000 α = 5% 100.0 100.0 97.2 97.8<br />
α = 10% 100.0 100.0 98.1 98.3<br />
II : Weak V<strong>ARMA</strong>(1,1) model (4.18)-(4.15) with θ0 = (4.19)