Deuxième Maîtrise, cours de Méthodes de l'Investigation Economique

Deuxième Maîtrise, cours de Méthodes de l'Investigation Economique EXERCICE N°2 : corrigé sommaire Contrôle de qualité : le diamètre des petits boulons pour la NASA |_read(econo\boulons.txt) x y
UNIT 88 IS NOW ASSIGNED TO: econo\boulons.txt ...SAMPLE RANGE IS NOW SET TO: 1 50
Pour vérifier que le four revient immédiatement à sa température
normale, il suffit de montrer que les écarts de température sont de moyenne
nulle et ne sont pas corrélées avec leurs valeurs passées. Deux méthodes
sont possibles. La première consiste en une inspection visuelle du
corrélogramme des écarts, qui devrait être uniformément plat. Pour
minimiser la taille du corrigé, je supprime les portions non-pertinentes
des résultats des commandes SHAZAM. |_arima x /plotac plotpac NET NUMBER OF OBSERVATIONS = 50
MEAN= 0.27662 VARIANCE= 1.6128 STANDARD DEV.= 1.2699 Remarquez que le moyenne (0.28) n'est pas significativement différente
de zéro (écart-type=1.27).
LAGS AUTOCORRELATIONS STD
ERR
1 -12 -.09 -.23 0.03 -.19 -.14 0.24 0.03 -.10 -.19 0.04 -.10 0.06
0.14
13 -24 0.18 0.14 -.07 -.08 -.16 0.10 0.04 0.06 0.06 -.18 -.21 0.14
0.17 LAGS PARTIAL AUTOCORRELATIONS STD ERR
1 -12 -.09 -.24 -.01 -.26 -.21 0.10 -.02 -.07 -.31 -.02 -.22 -.08
0.14 0 0 0
AUTOCORRELATION FUNCTION OF THE SERIES (1-B) (1-B ) X 1 -.09 . + RRRR +
.
2 -.23 . + RRRRRRRRR +
.
3 0.03 . + RR +
.
4 -.19 . + RRRRRRR +
.
5 -.14 . + RRRRRR +
.
6 0.24 . + RRRRRRRRR +
.
7 0.03 . + RR +
.
8 -.10 . + RRRR +
.
9 -.19 . + RRRRRRR +
.
10 0.04 . + RR +
.
11 -.10 . + RRRR +
.
12 0.06 . + RRR +
.
13 0.18 . + RRRRRRR +
.
14 0.14 . + RRRRRR +
.
15 -.07 . + RRRR +
.
16 -.08 . + RRRR +
.
17 -.16 . + RRRRRRR +
.
18 0.10 . + RRRR +
.
19 0.04 . + RR +
.
20 0.06 . + RRR +
.
21 0.06 . + RRR +
.
22 -.18 . + RRRRRRR +
.
23 -.21 . + RRRRRRRR +
.
24 0.14 . + RRRRRR +
.
0 0 0
PARTIAL AUTOCORRELATION FUNCTION OF THE SERIES (1-B) (1-B ) X 1 -.09 . + RRRR +
.
2 -.24 . + RRRRRRRRR +
.
3 -.01 . + RR +
.
4 -.26 . +RRRRRRRRRR +
.
5 -.21 . + RRRRRRRR +
.
6 0.10 . + RRRR +
.
7 -.02 . + RR +
.
8 -.07 . + RRR +
.
9 -.31 . RRRRRRRRRRRR +
.
10 -.02 . + RR +
.
11 -.22 . + RRRRRRRR +
.
12 -.08 . + RRRR +
.
|_sample 2 50
|_genr bx = lag(x) La deuxième méthode consiste à estimer l'équation suivante : xt = ( +
( xt-1 + ut . Les coefficients ( et ( ne devraient pas être
significativement différents de zéro. Attention : l'inférence statistique
sur ( et ( suppose que les hypothèses Gauss-Markov sont vérifiées ; il faut
donc soumettre cette régression à tous les tests classiques (auto-
corrélation des résidus, hétéroscédasticité, normalité des résidus,...)[1] |_ols x bx /rstat gf lm R-SQUARE = 0.0080 R-SQUARE ADJUSTED = -0.0131
VARIANCE OF THE ESTIMATE-SIGMA**2 = 1.6647
STANDARD ERROR OF THE ESTIMATE-SIGMA = 1.2902
SUM OF SQUARED ERRORS-SSE= 78.242
MEAN OF DEPENDENT VARIABLE = 0.28442
LOG OF THE LIKELIHOOD FUNCTION = -80.9937
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED
ELASTICITY
NAME COEFFICIENT ERROR 47 DF P-VALUE CORR. COEFFICIENT AT
MEANS
BX -0.91666E-01 0.1486 -0.6170 0.540-0.090 -0.0896
-0.0768
CONSTANT 0.30626 0.1877 1.632 0.109 0.232 0.0000
1.0768 DURBIN-WATSON = 1.9666 VON NEUMANN RATIO = 2.0076 RHO = -0.01472
RESIDUAL SUM = 0.13323E-14 RESIDUAL VARIANCE = 1.6647
SUM OF ABSOLUTE ERRORS= 49.700
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.0080
RUNS TEST: 23 RUNS, 25 POS, 0 ZERO, 24 NEG NORMAL STATISTIC =
-0.7192
COEFFICIENT OF SKEWNESS = -0.0430 WITH STANDARD DEVIATION OF 0.3398
COEFFICIENT OF EXCESS KURTOSIS = -0.5628 WITH STANDARD DEVIATION OF 0.6681 GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 6 GROUPS
OBSERVED 0.0 9.0 15.0 16.0 8.0 1.0
EXPECTED 1.1 6.7 16.7 16.7 6.7 1.1
CHI-SQUARE = 2.4314 WITH 2 DEGREES OF FREEDOM JARQUE-BERA ASYMPTOTIC LM NORMALITY TEST
CHI-SQUARE = 0.8169 WITH 2 DEGREES OF FREEDOM |_diagnos /acf het HETEROSKEDASTICITY TESTS
E**2 ON YHAT: CHI-SQUARE = 2.068 WITH 1 D.F.
E**2 ON YHAT**2: CHI-SQUARE = 1.764 WITH 1 D.F.
E**2 ON LOG(YHAT**2): CHI-SQUARE = 2.027 WITH 1 D.F.
E**2 ON X (B-P-G) TEST: CHI-SQUARE = 2.068 WITH 1 D.F.
E**2 ON LAG(E**2) ARCH TEST: CHI-SQUARE = 0.013 WITH 1 D.F.
LOG(E**2) ON X (HARVEY) TEST: CHI-SQUARE = 3.795 WITH 1 D.F.
ABS(E) ON X (GLEJSER) TEST: CHI-SQUARE = 3.060 WITH 1 D.F. RESIDUAL CORRELOGRAM
LM-TEST FOR HJ:RHO(J)=0, STATISTIC IS STANDARD NORMAL
LAG RHO STD ERR T-STAT LM-STAT DW-TEST BOX-PIERCE-
LJUNG
1 -0.0142 0.1429 -0.0994 1.0280 1.9666 0.0105
2 -0.2341 0.1429 -1.6384 1.7376 2.3295 2.9232
3 -0.0049 0.1429 -0.0340 0.0371 1.8673 2.9245
4 -0.2000 0.1429 -1.4001 1.4884 2.2520 5.1460
5 -0.1348 0.1429 -0.9439 1.0315 2.1195 6.1788
6 0.2464 0.1429 1.7245 1.8499 1.3090 9.7061
7 0.0370 0.1429 0.2587 0.2884 1.6869 9.7874
8 -0.1185 0.1429 -0.8292 0.8969 1.9879 10.6427
9 -0.1886 0.1429 -1.3204 1.4507 2.0969 12.8656
10 0.0069 0.1429 0.0483 0.0538 1.6447 12.8686
11 -0.0911 0.1429 -0.6376 0.7041 1.8264 13.4142
12 0.0871 0.1429 0.6095 0.6900 1.3219 13.9262
13 0.1911 0.1429 1.3378 1.5315 1.0552 16.4617
14 0.1400 0.1429 0.9803 1.1460 1.0919 17.8620
15 -0.0747 0.1429 -0.5226 0.6063 1.5126 18.2716
LM CHI-SQUARE STATISTIC WITH 15 D.F. IS 14.823 Nous sommes maintenant prêts à étudier la relation entre circonférence
des boulons et température du four. On retiendra une spécification linéaire
sur base de l'inspection visuelle du nuage de points.
|_sample 1 50 |_ols y x /rstat gf lm dwpvalue DURBIN-WATSON STATISTIC = 0.58235
DURBIN-WATSON P-VALUE = 0.000000 R-SQUARE = 0.0045 R-SQUARE ADJUSTED = -0.0162
VARIANCE OF THE ESTIMATE-SIGMA**2 = 3.3250
STANDARD ERROR OF THE ESTIMATE-SIGMA = 1.8235
SUM OF SQUARED ERRORS-SSE= 159.60
MEAN OF DEPENDENT VARIABLE = 14.893
LOG OF THE LIKELIHOOD FUNCTION = -99.9629
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED
ELASTICITY
NAME COEFFICIENT ERROR 48 DF P-VALUE CORR. COEFFICIENT AT
MEANS
X 0.95944E-01 0.2051 0.4677 0.642 0.067 0.0674
0.0018
CONSTANT 14.867 0.2640 56.30 0.000 0.993 0.0000
0.9982 DURBIN-WATSON = 0.5824 VON NEUMANN RATIO = 0.5942 RHO = 0.69950
RESIDUAL SUM = -0.66613E-15 RESIDUAL VARIANCE = 3.3250
SUM OF ABSOLUTE ERRORS= 73.336
R-SQUARE BETWEEN OBSERVED AND PREDICTED = 0.0045
RUNS TEST: 9 RUNS, 27 POS, 0 ZERO, 23 NEG NORMAL STATISTIC =
-4.8441
COEFFICIENT OF SKEWNESS = -0.0323 WITH STANDARD DEVIATION OF 0.3366
COEFFICIENT OF EXCESS KURTOSIS = -0.3756 WITH STANDARD DEVIATION OF 0.6619 GOODNESS OF FIT TEST FOR NORMALITY OF RESIDUALS - 6 GROUPS
OBSERVED 1.0 7.0 15.0 21.0 5.0 1.0
EXPECTED 1.1 6.8 17.1 17.1 6.8 1.1
CHI-SQUARE = 1.6720 WITH 2 DEGREES OF FREEDOM JARQUE-BERA ASYMPTOTIC LM NORMALITY TEST
CHI-SQUARE = 0.4428 WITH 2 DEGREES OF FREEDOM
|_diagnos /acf het HETEROSKEDASTICITY TESTS
E**2 ON YHAT: CHI-SQUARE = 0.989 WITH 1 D.F.
E**2 ON YHAT**2: CHI-SQUARE = 0.994 WITH 1 D.F.
E**2 ON LOG(YHAT**2): CHI-SQUARE = 0.984 WITH 1 D.F.
E**2 ON X (B-P-G) TEST: CHI-SQUARE = 0.989 WITH 1 D.F.
E**2 ON LAG(E**2) ARCH TEST: CHI-SQUARE = 0.815 WITH 1 D.F.
LOG(E**2) ON X (HARVEY) TEST: CHI-SQUARE = 1.254 WITH 1 D.F.
ABS(E) ON X (GLEJSER) TEST: CHI-SQUARE = 0.440 WITH 1 D.F. RESIDUAL CORRELOGRAM
LM-TEST FOR HJ:RHO(J)=0, STATISTIC IS STANDARD NORMAL
LAG RHO STD ERR T-STAT LM-STAT DW-TEST BOX-PIERCE-
LJUNG
1 0.6982 0.1414 4.9369 4.9498 0.5824 25.8655
2 0.5499 0.1414 3.8882 4.0001 0.8403 42.2433
3 0.4694 0.1414 3.3194 3.4403 0.9472 54.4341
4 0.2913 0.1414 2.0598 2.2456 1.2859 59.2305
5 0.0536 0.1414 0.3791 0.3990 1.7454 59.3965
6