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

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Chapitre 2. Estimating weak structural VARMA models 68 Table 2.2 – Empirical power of standard and modified tests : relative frequencies (in %) of rejection of H0 : b1(2,2) = 0. The number of replications is N = 1000. Model Length n Level Standard Test Modified Test Wald LM LR Wald LM LR α = 1% 6.8 5.9 6.6 8.0 6.5 7.9 III n = 500 α = 5% 20.5 19.4 20.4 21.6 20.1 21.7 α = 10% 29.5 29.0 29.4 30.6 29.5 30.6 α = 1% 1.7 1.8 1.7 15.5 14.3 15.6 IV n = 500 α = 5% 11.4 9.4 10.1 35.1 34.0 35.0 α = 10% 21.1 20.2 20.6 47.1 44.9 46.8 III : Strong VARMA(1,1) model (2.9)-(2.10) with ϑ0 = (0.95,2,0.05) IV : Weak VARMA(1,1) model (2.9)-(2.11) with ϑ0 = (0.95,2,0.05)
1(2, 2) − b ^ 1(2, 2) Density Chapitre 2. Estimating weak structural VARMA models 69 −0.05 0.05 −0.08 −0.02 0.04 0 5 10 15 Strong VARMA (a) (b) (c) estimation errors for n=2000 Strong case: Normal Q−Q Plot of b ^ 1(2, 2) −3 −2 −1 0 1 2 3 Normal quantiles Strong case −0.05 0.00 0.05 Distribution of b1(2, 2) − b ^ 1(2, 2) b1(2, 2) − b ^ 1(2, 2) Density −0.05 0.05 −0.04 0.00 0.04 0 5 10 20 Weak VARMA (a) (b) (c) estimation errors for n=2000 Weak case: Normal Q−Q Plot of b ^ 1(2, 2) −3 −2 −1 0 1 2 3 Normal quantiles Weak case −0.04 −0.02 0.00 0.02 0.04 Distribution of b1(2, 2) − b ^ 1(2, 2) Figure 2.1 – QMLE of N = 1,000 independent simulations of the VARMA(1,1) model (2.9) with size n = 2,000 and unknown parameter ϑ0 = ((a1(2,2),b1(2,1),b1(2,2)) = (0.95,2,0), when the noise is strong (left panels) and when the noise is the weak noise (2.11) (right panels). Points (a)-(c), in the box-plots of the top panels, display the distribution of the estimation errors ˆ ϑ(i)−ϑ0(i) for i = 1,2,3. The panels of the middle present the Q-Q plot of the estimates ˆ ϑ(3) = ˆ b1(2,2) of the last parameter. The bottom panels display the distribution of the same estimates. The kernel density estimate is displayed in full line, and the centered Gaussian density with the same variance is plotted in dotted line.
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UNIVERSITÉ CHARLES DE GAULLE - LIL
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Résumé Dans cette thèse nous él
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Abstract The goal of this thesis is
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Table des matières Résumé ii Abs
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4.6 Limiting distribution of the po
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4.12 Empirical size (in %) of the s
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Chapitre 1 Introduction Lorsque l
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Chapitre 1. Introduction 3 Pour les
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Chapitre 1. Introduction 5 VARMA(p0
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Chapitre 1. Introduction 7 obtenir
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Chapitre 1. Introduction 9 les outi
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Chapitre 1. Introduction 11 1.1.1 E
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Chapitre 1. Introduction 13 Propri
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Chapitre 1. Introduction 15 H7 : Po
Page 29 and 30: Chapitre 1. Introduction 17 Défini
Page 31 and 32: Chapitre 1. Introduction 19 où λ
Page 33 and 34: Chapitre 1. Introduction 21 Remarqu
Page 35 and 36: Chapitre 1. Introduction 23 où Eij
Page 37 and 38: Chapitre 1. Introduction 25 La dém
Page 39 and 40: Chapitre 1. Introduction 27 Théor
Page 41 and 42: Chapitre 1. Introduction 29 La sél
Page 43 and 44: Chapitre 1. Introduction 31 La dém
Page 45 and 46: Chapitre 1. Introduction 33 de BP d
Page 47 and 48: Chapitre 1. Introduction 35 Théor
Page 49 and 50: Chapitre 1. Introduction 37 Les exp
Page 51 and 52: Chapitre 1. Introduction 39 indispe
Page 53 and 54: Chapitre 1. Introduction 41 Lemme 1
Page 55 and 56: Chapitre 1. Introduction 43 En util
Page 57 and 58: Chapitre 1. Introduction 45 I11 = 2
Page 59 and 60: Chapitre 1. Introduction 47 ceux-ci
Page 61 and 62: Chapitre 1. Introduction 49 Remarqu
Page 63 and 64: Références bibliographiques Ahn,
Page 65 and 66: Chapitre 1. Introduction 53 Hannan,
Page 67 and 68: Chapitre 2 Estimating structural VA
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Page 101 and 102: Chapitre 3. Estimating the asymptot
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Chapitre 4. Multivariate portmantea
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Chapitre 5. Model selection of weak
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