Apres avoir effectué ce
test on aura le résultat suivant :
1- test de L-Jung box
(View -Residual tests-corelogram Q-stat)
On remarque que tous les pics sont à l'intérieur
de l'intervalle de confiance c'est à dire ces résidus constituent
un bruit blanc, on confirme par le test de L-JUNG BOX, on
trouve Q-stat<X2(N-p-q).
Q-STAT=16.478<28.86=X (16) X
(16)=khi-deux de 16 degré de liberté.
2-test de Jarque et Berra :
Pour savoir si les résidus forment un bruit
blanc gaussien on applique le test de Jarques et
Berra.
· Le test de normalité :
S= suit une loi de Khi deux
Avec : Sk : le coefficient de Skewness
Ku : le coefficient de Kurtoisis
La statistique de Jarques et Berra (s=2.49)>x2 au
seuil de 5%
Par conséquent on rejette l'hypothèse de
normalité des résidus
On peut dire que le bruit blanc n'est pas gaussien
comme le montre
Le Jarque-Berra est une statistique de test pour examiner si la
série est normalement distribuée. La statistique mesure la
différence du Skewness et du Kurtosis de la série avec ceux de la
distribution normale
3- Test de l'effet ARCH:
|
Heteroskedasticity Test: ARCH
|
|
|
|
|
|
|
|
|
|
|
|
|
|
F-statistic
|
3.024388
|
Prob. F(1,120)
|
0.0846
|
|
Obs*R-squared
|
2.999205
|
Prob. Chi-Square(1)
|
0.0833
|
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|
Test Equation:
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Dependent Variable: RESID^2
|
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Method: Least Squares
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|
Date: 06/13/10 Time: 16:40
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|
|
Sample: 2000M02 2010M03
|
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|
|
Included observations: 122
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
C
|
0.001931
|
0.000268
|
7.198444
|
0.0000
|
|
RESID^2(-1)
|
0.035081
|
0.020172
|
1.739077
|
0.0846
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.024584
|
Mean dependent var
|
0.001959
|
|
Adjusted R-squared
|
0.016455
|
S.D. dependent var
|
0.002982
|
|
S.E. of regression
|
0.002958
|
Akaike info criterion
|
-8.792651
|
|
Sum squared resid
|
0.001050
|
Schwarz criterion
|
-8.746684
|
|
Log likelihood
|
538.3517
|
Hannan-Quinn critter.
|
-8.773981
|
|
F-statistic
|
3.024388
|
Durbin-Watson stat
|
1.201956
|
|
Prob(F-statistic)
|
0.084586
|
|
|
|
|
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|
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|
D'après les probabilités de signification
(0.0846>0.05) et (0.0833>0.05) on déduire l'absence de l'effet
ARCH c'est à dire la variance des résidus sont
homogènes.
· Corrélogramme des résidus
au carrées :
On remarque que tous les pics sont à
l'intérieur de l'intervalle de confiance ce qui confirme l'absence de
l'effet ARCH.
On peut aussi tester l'effet ARCH
d'après le coefficient de Kurtoisis, si Ku>3 il
existe l'effet ARCH, dans notre exemple KU=3.32>3.
Ø Prévision :
L'objectif de la méthode de Box & Jenkins est
de réaliser des prévisions. Une fois que le
modèle AR< M A (p, d, q) a été choisi, estime et valide
pour les observations X1, ...., Xt, on calcule les prévisions. On
suppose qu'on se trouve à l' instant t, et qu'on désir
prévoir la valeur de x t+ h, tel que alors on utilise l'estimateur
XX t(h) l'espérance conditionnelle de Xt+ h
Les valeurs de la prévision suivent une droite
linéaire.
ANNEXES
|
ANNEXE 1 :
|
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|
|
DATE
|
VALUE
|
|
|
1999-01-01
|
1,1591
|
|
|
1999-02-01
|
1,1203
|
|
|
1999-03-01
|
1,0886
|
|
|
1999-04-01
|
1,0701
|
|
|
1999-05-01
|
1,0630
|
|
|
1999-06-01
|
1,0377
|
|
|
1999-07-01
|
1,0370
|
|
|
1999-08-01
|
1,0605
|
|
|
1999-09-01
|
1,0497
|
|
|
1999-10-01
|
1,0706
|
|
|
1999-11-01
|
1,0328
|
|
|
1999-12-01
|
1,0110
|
|
|
2000-01-01
|
1,0131
|
|
|
2000-02-01
|
0,9834
|
|
|
2000-03-01
|
0,9643
|
|
|
2000-04-01
|
0,9449
|
|
|
2000-05-01
|
0,9059
|
|
|
2000-06-01
|
0,9505
|
|
|
2000-07-01
|
0,9386
|
|
|
2000-08-01
|
0,9045
|
|
|
2000-09-01
|
0,8695
|
|
|
2000-10-01
|
0,8525
|
|
|
2000-11-01
|
0,8552
|
|
|
2000-12-01
|
0,8983
|
|
|
2001-01-01
|
0,9376
|
|
|
2001-02-01
|
0,9205
|
|
|
2001-03-01
|
0,9083
|
|
|
2001-04-01
|
0,8925
|
|
|
2001-05-01
|
0,8753
|
|
|
2001-06-01
|
0,8530
|
|
|
2001-07-01
|
0,8615
|
|
|
2001-08-01
|
0,9014
|
|
|
2001-09-01
|
0,9114
|
|
|
2001-10-01
|
0,9050
|
|
|
2001-11-01
|
0,8883
|
|
|
2001-12-01
|
0,8912
|
|
|
2002-01-01
|
0,8832
|
|
|
2002-02-01
|
0,8707
|
|
|
2002-03-01
|
0,8766
|
|
|
2002-04-01
|
0,8860
|
|
|
2002-05-01
|
0,9170
|
|
|
2002-06-01
|
0,9561
|
|
|
2002-07-01
|
0,9935
|
|
|
2002-08-01
|
0,9781
|
|
|
2002-09-01
|
0,9806
|
|
|
2002-10-01
|
0,9812
|
|
|
2002-11-01
|
1,0013
|
|
|
2002-12-01
|
1,0194
|
|
|
2003-01-01
|
1,0622
|
|
|
2003-02-01
|
1,0785
|
|
|
2003-03-01
|
1,0797
|
|
|
2003-04-01
|
1,0862
|
|
|
2003-05-01
|
1,1556
|
|
|
2003-06-01
|
1,1674
|
|
|
2003-07-01
|
1,1365
|
|
|
2003-08-01
|
1,1155
|
|
|
2003-09-01
|
1,1267
|
|
|
2003-10-01
|
1,1714
|
|
|
2003-11-01
|
1,1710
|
|
|
2003-12-01
|
1,2298
|
|
|
2004-01-01
|
1,2638
|
|
|
2004-02-01
|
1,2640
|
|
|
2004-03-01
|
1,2261
|
|
|
2004-04-01
|
1,1989
|
|
|
2004-05-01
|
1,2000
|
|
|
2004-06-01
|
1,2146
|
|
|
2004-07-01
|
1,2266
|
|
|
2004-08-01
|
1,2191
|
|
|
2004-09-01
|
1,2224
|
|
|
2004-10-01
|
1,2507
|
|
|
2004-11-01
|
1,2997
|
|
|
2004-12-01
|
1,3406
|
|
|
2005-01-01
|
1,3123
|
|
|
2005-02-01
|
1,3013
|
|
|
2005-03-01
|
1,3185
|
|
|
2005-04-01
|
1,2943
|
|
|
2005-05-01
|
1,2697
|
|
|
2005-06-01
|
1,2155
|
|
|
2005-07-01
|
1,2041
|
|
|
2005-08-01
|
1,2295
|
|
|
2005-09-01
|
1,2234
|
|
|
2005-10-01
|
1,2022
|
|
|
2005-11-01
|
1,1789
|
|
|
2005-12-01
|
1,1861
|
|
|
2006-01-01
|
1,2126
|
|
|
2006-02-01
|
1,1940
|
|
|
2006-03-01
|
1,2028
|
|
|
2006-04-01
|
1,2273
|
|
|
2006-05-01
|
1,2767
|
|
|
2006-06-01
|
1,2661
|
|
|
2006-07-01
|
1,2681
|
|
|
2006-08-01
|
1,2810
|
|
|
2006-09-01
|
1,2722
|
|
|
2006-10-01
|
1,2617
|
|
|
2006-11-01
|
1,2888
|
|
|
2006-12-01
|
1,3205
|
|
|
2007-01-01
|
1,2993
|
|
|
2007-02-01
|
1,3080
|
|
|
2007-03-01
|
1,3246
|
|
|
2007-04-01
|
1,3513
|
|
|
2007-05-01
|
1,3518
|
|
|
2007-06-01
|
1,3421
|
|
|
2007-07-01
|
1,3726
|
|
|
2007-08-01
|
1,3626
|
|
|
2007-09-01
|
1,3910
|
|
|
2007-10-01
|
1,4233
|
|
|
2007-11-01
|
1,4683
|
|
|
2007-12-01
|
1,4559
|
|
|
2008-01-01
|
1,4728
|
|
|
2008-02-01
|
1,4759
|
|
|
2008-03-01
|
1,5520
|
|
|
2008-04-01
|
1,5754
|
|
|
2008-05-01
|
1,5554
|
|
|
2008-06-01
|
1,5562
|
|
|
2008-07-01
|
1,5759
|
|
|
2008-08-01
|
1,4955
|
|
|
2008-09-01
|
1,4342
|
|
|
2008-10-01
|
1,3266
|
|
|
2008-11-01
|
1,2744
|
|
|
2008-12-01
|
1,3511
|
|
|
2009-01-01
|
1,3244
|
|
|
2009-02-01
|
1,2797
|
|
|
2009-03-01
|
1,3050
|
|
|
2009-04-01
|
1,3199
|
|
|
2009-05-01
|
1,3646
|
|
|
2009-06-01
|
1,4014
|
|
|
2009-07-01
|
1,4092
|
|
|
2009-08-01
|
1,4266
|
|
|
2009-09-01
|
1,4575
|
|
|
2009-10-01
|
1,4821
|
|
|
2009-11-01
|
1,4908
|
|
|
2009-12-01
|
1,4579
|
|
|
2010-01-01
|
1,4266
|
|
|
2010-02-01
|
1,3680
|
|
|
2010-03-01
|
1,3570
|
|
ANNEXE2:
|
Dependent Variable: STATIONNAIRE
|
|
|
Method: Least Squares
|
|
|
|
Date: 06/13/10 Time: 17:28
|
|
|
|
Sample (adjusted): 2000M02 2010M03
|
|
|
Included observations: 122 after adjustments
|
|
|
Convergence achieved after 2 iterations
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
AR(1)
|
0.927749
|
0.032615
|
28.44562
|
0.0000
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.869902
|
Mean dependent var
|
0.001160
|
|
Adjusted R-squared
|
0.869902
|
S.D. dependent var
|
0.123202
|
|
S.E. of regression
|
0.044438
|
Akaike info criterion
|
-3.381294
|
|
Sum squared resid
|
0.238940
|
Schwarz criterion
|
-3.358310
|
|
Log likelihood
|
207.2589
|
Hannan-Quinn criter.
|
-3.371958
|
|
Durbin-Watson stat
|
1.306086
|
|
|
|
ANNEXE3 :
|
Dependent Variable: STATIONNAIRE
|
|
|
Method: Least Squares
|
|
|
|
Date: 06/13/10 Time: 16:12
|
|
|
|
Sample (adjusted): 2000M02 2010M03
|
|
|
Included observations: 122 after adjustments
|
|
|
Convergence achieved after 2 iterations
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
AR(1)
|
0.927749
|
0.032615
|
28.44562
|
0.0000
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.869902
|
Mean dependent var
|
0.001160
|
|
Adjusted R-squared
|
0.869902
|
S.D. dependent var
|
0.123202
|
|
S.E. of regression
|
0.044438
|
Akaike info criterion
|
-3.381294
|
|
Sum squared resid
|
0.238940
|
Schwarz criterion
|
-3.358310
|
|
Log likelihood
|
207.2589
|
Hannan-Quinn criter.
|
-3.371958
|
|
Durbin-Watson stat
|
1.306086
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Inverted AR Roots
|
.93
|
|
|
|
|
|
|
|
|
|
|
|
|
ANNEXE4:
|
Dependent Variable: VALUESA
|
|
|
|
Method: Least Squares
|
|
|
|
Date: 06/13/10 Time: 16:04
|
|
|
|
Sample (adjusted): 2000M01 2010M03
|
|
|
Included observations: 123 after adjustments
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
C
|
-0.012010
|
0.025537
|
-0.470286
|
0.6390
|
|
@TREND
|
0.000628
|
0.000315
|
1.996130
|
0.0482
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.031880
|
Mean dependent var
|
0.033831
|
|
Adjusted R-squared
|
0.023879
|
S.D. dependent var
|
0.125383
|
|
S.E. of regression
|
0.123877
|
Akaike info criterion
|
-1.322926
|
|
Sum squared resid
|
1.856812
|
Schwarz criterion
|
-1.277199
|
|
Log likelihood
|
83.35993
|
Hannan-Quinn criter.
|
-1.304352
|
|
F-statistic
|
3.984533
|
Durbin-Watson stat
|
0.133902
|
|
Prob(F-statistic)
|
0.048165
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Conclusion générale
|
|
