data.docx (1) Means, standard deviations and correlations The dataset is: new09.in7 The sample is: 1973(4) - 1990(2) Means LBelgium LFrance LGermanyLFrance/BelgiumLFrance/GermanyLBelgium/Germany 3.8105 3.7169 3.9794 -1.9465 0.92657 2.8731 Standard deviations (using T-1) LBelgium LFrance LGermanyLFrance/BelgiumLFrance/GermanyLBelgium/Germany 0.29047 0.42521 0.17195 0.10754 0.23542 0.13881 Correlation matrix: LBelgium LFrance LGermanyLFrance/Belgium LBelgium 1.0000 0.99593 0.99555 0.92029 LFrance 0.99593 1.0000 0.99782 0.91758 LGermany 0.99555 0.99782 1.0000 0.91119 LFrance/Belgium 0.92029 0.91758 0.91119 1.0000 LFrance/Germany 0.97657 0.98038 0.97257 0.94242 LBelgium/Germany 0.94326 0.95181 0.94353 0.82359 LFrance/GermanyLBelgium/Germany LBelgium 0.97657 0.94326 LFrance 0.98038 0.95181 LGermany 0.97257 0.94353 LFrance/Belgium 0.94242 0.82359 LFrance/Germany 1.0000 0.96585 LBelgium/Germany 0.96585 1.0000 Normality tests and descriptive statistics The dataset is: new09.in7 The sample is: 1973(5) - 1990(2) Normality test for DLBelgium Observations 202 Mean 0.0049006 Std.Devn. 0.0040206 Skewness 0.55869 Excess Kurtosis -0.35971 Minimum -0.0029746 Maximum 0.016097 Asymptotic test: Chi^2(2) = 11.597 [0.0030]** Normality test: Chi^2(2) = 23.525 [0.0000]** Normality test for DLFrance Observations 202 Mean 0.0067183 Std.Devn. 0.0037830 Skewness 0.28292 Excess Kurtosis -0.22797 Minimum -0.0024968 Maximum 0.019186 Asymptotic test: Chi^2(2) = 3.1322 [0.2089] Normality test: Chi^2(2) = 3.9005 [0.1422] Normality test for DLGermany Observations 202 Mean 0.0028933 Std.Devn. 0.0030606 Skewness 0.59041 Excess Kurtosis 0.35519 Minimum -0.0033465 Maximum 0.012716 Asymptotic test: Chi^2(2) = 12.798 [0.0017]** Normality test: Chi^2(2) = 12.800 [0.0017]** Normality test for DLFrance/Belgium Observations 202 Mean 0.0017844 Std.Devn. 0.011918 Skewness 0.48711 Excess Kurtosis 4.8743 Minimum -0.055216 Maximum 0.043456 Asymptotic test: Chi^2(2) = 207.95 [0.0000]** Normality test: Chi^2(2) = 83.018 [0.0000]** Normality test for DLFrance/Germany Observations 202 Mean 0.0037082 Std.Devn. 0.012603 Skewness 1.0110 Excess Kurtosis 3.1420 Minimum -0.038558 Maximum 0.050134 Asymptotic test: .

1. data.docx
(1)
Means, standard deviations and correlations
The dataset is: new09.in7
The sample is: 1973(4) - 1990(2)
Means
LBelgium LFrance
LGermanyLFrance/BelgiumLFrance/GermanyLBelgium/German
y
3.8105 3.7169 3.9794 -1.9465 0.92657
2.8731
Standard deviations (using T-1)
LBelgium LFrance
LGermanyLFrance/BelgiumLFrance/GermanyLBelgium/German
y
0.29047 0.42521 0.17195 0.10754 0.23542
0.13881
Correlation matrix:
LBelgium LFrance
LGermanyLFrance/Belgium
LBelgium 1.0000 0.99593 0.99555 0.92029
LFrance 0.99593 1.0000 0.99782 0.91758
LGermany 0.99555 0.99782 1.0000 0.91119
LFrance/Belgium 0.92029 0.91758 0.91119
1.0000
LFrance/Germany 0.97657 0.98038 0.97257
0.94242
LBelgium/Germany 0.94326 0.95181 0.94353
0.82359
LFrance/GermanyLBelgium/Germany
LBelgium 0.97657 0.94326
LFrance 0.98038 0.95181
LGermany 0.97257 0.94353

2. LFrance/Belgium 0.94242 0.82359
LFrance/Germany 1.0000 0.96585
LBelgium/Germany 0.96585 1.0000
Normality tests and descriptive statistics
The dataset is: new09.in7
The sample is: 1973(5) - 1990(2)
Normality test for DLBelgium
Observations 202
Mean 0.0049006
Std.Devn. 0.0040206
Skewness 0.55869
Excess Kurtosis -0.35971
Minimum -0.0029746
Maximum 0.016097
Asymptotic test: Chi^2(2) = 11.597 [0.0030]**
Normality test: Chi^2(2) = 23.525 [0.0000]**
Normality test for DLFrance
Observations 202
Mean 0.0067183
Std.Devn. 0.0037830
Skewness 0.28292
Excess Kurtosis -0.22797
Minimum -0.0024968
Maximum 0.019186
Asymptotic test: Chi^2(2) = 3.1322 [0.2089]
Normality test: Chi^2(2) = 3.9005 [0.1422]
Normality test for DLGermany
Observations 202
Mean 0.0028933
Std.Devn. 0.0030606
Skewness 0.59041
Excess Kurtosis 0.35519

3. Minimum -0.0033465
Maximum 0.012716
Asymptotic test: Chi^2(2) = 12.798 [0.0017]**
Normality test: Chi^2(2) = 12.800 [0.0017]**
Normality test for DLFrance/Belgium
Observations 202
Mean 0.0017844
Std.Devn. 0.011918
Skewness 0.48711
Excess Kurtosis 4.8743
Minimum -0.055216
Maximum 0.043456
Asymptotic test: Chi^2(2) = 207.95 [0.0000]**
Normality test: Chi^2(2) = 83.018 [0.0000]**
Normality test for DLFrance/Germany
Observations 202
Mean 0.0037082
Std.Devn. 0.012603
Skewness 1.0110
Excess Kurtosis 3.1420
Minimum -0.038558
Maximum 0.050134
Asymptotic test: Chi^2(2) = 117.50 [0.0000]**
Normality test: Chi^2(2) = 28.248 [0.0000]**
Normality test for DLBelgium/Germany
Observations 202
Mean 0.0019238
Std.Devn. 0.0078273
Skewness 4.2544
Excess Kurtosis 31.142
Minimum -0.018404
Maximum 0.069908
Asymptotic test: Chi^2(2) = 8772.2 [0.0000]**

4. Normality test: Chi^2(2) = 415.61 [0.0000]**
(2) Unit-root test
Stationary
EQ( 1) Modelling DLFrance by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant -0.0160450 0.007638 -2.10 0.0369 0.0217
Trend -0.000107278 1.858e-005 -5.77 0.0000 0.1435
LFrance_1 0.00908918 0.002558 3.55 0.0005
0.0597
sigma 0.00279924 RSS 0.00155930985
R^2 0.460593 F(2,199) = 84.96 [0.000]**
log-likelihood 902.324 DW 1.08
no. of observations 202 no. of parameters 3
mean(DLFrance) 0.00671834 var(DLFrance) 1.43108e-005
// Batch code for EQ( 1)
module("PcGive");
package("PcGive", "Single-equation");
usedata("new09.in7");
system
{
Y = DLFrance;
Z = Constant, Trend, LFrance_1;
}
estimate("OLS", 1973, 5, 1990, 2);
EQ( 2) Modelling DLFrance by OLS
The dataset is: new09.in7

5. The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0269034 0.001874 14.4 0.0000 0.5076
LFrance_1 -0.00543452 0.0005012 -10.8 0.0000
0.3702
sigma 0.00301714 RSS 0.00182062088
R^2 0.370198 F(1,200) = 117.6 [0.000]**
log-likelihood 886.676 DW 0.911
no. of observations 202 no. of parameters 2
mean(DLFrance) 0.00671834 var(DLFrance) 1.43108e-005
EQ( 3) Modelling DLFrance by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LFrance_1 0.00171584 8.072e-005 21.3 0.0000
0.6921
sigma 0.00428889 RSS 0.00369731806
log-likelihood 815.124 DW 0.452
no. of observations 202 no. of parameters 1
mean(DLFrance) 0.00671834 var(DLFrance) 1.43108e-005
EQ( 4) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0215108 0.01391 1.55 0.1235 0.0119
Trend -1.75107e-005 2.083e-005 -0.841 0.4015
0.0035
LBelgium_1 -0.00388990 0.004198 -0.927 0.3553
0.0043

6. sigma 0.00343212 RSS 0.00234411488
R^2 0.282144 F(2,199) = 39.11 [0.000]**
log-likelihood 861.15 DW 1.34
no. of observations 202 no. of parameters 3
mean(DLBelgium) 0.00490063 var(DLBelgium) 1.61655e-
005
EQ( 5) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0328908 0.003186 10.3 0.0000 0.3476
LBelgium_1 -0.00734906 0.0008341 -8.81 0.0000
0.2796
sigma 0.00342961 RSS 0.00235244174
R^2 0.279594 F(1,200) = 77.62 [0.000]**
log-likelihood 860.792 DW 1.33
no. of observations 202 no. of parameters 2
mean(DLBelgium) 0.00490063 var(DLBelgium) 1.61655e-
005
EQ( 6) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LBelgium_1 0.00123717 7.802e-005 15.9 0.0000
0.5557
sigma 0.00423554 RSS 0.00360589874
log-likelihood 817.653 DW 0.874
no. of observations 202 no. of parameters 1
mean(DLBelgium) 0.00490063 var(DLBelgium) 1.61655e-

7. 005
EQ( 7) Modelling DLGermany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0218191 0.01885 1.16 0.2484 0.0067
Trend -6.70422e-006 1.501e-005 -0.447 0.6557
0.0010
LGermany_1 -0.00458449 0.005113 -0.897 0.3710
0.0040
sigma 0.00284988 RSS 0.00161623889
R^2 0.145862 F(2,199) = 16.99 [0.000]**
log-likelihood 898.702 DW 1.26
no. of observations 202 no. of parameters 3
mean(DLGermany) 0.00289333 var(DLGermany) 9.36755e-
006
EQ( 8) Modelling DLGermany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0299740 0.004654 6.44 0.0000 0.1718
LGermany_1 -0.00680706 0.001169 -5.82 0.0000
0.1450
sigma 0.00284417 RSS 0.00161785847
R^2 0.145006 F(1,200) = 33.92 [0.000]**
log-likelihood 898.601 DW 1.26
no. of observations 202 no. of parameters 2
mean(DLGermany) 0.00289333 var(DLGermany) 9.36755e-
006

8. EQ( 9) Modelling DLGermany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LGermany_1 0.000713342 5.508e-005 13.0 0.0000
0.4549
sigma 0.00311743 RSS 0.00195338812
log-likelihood 879.567 DW 1.05
no. of observations 202 no. of parameters 1
mean(DLGermany) 0.00289333 var(DLGermany) 9.36755e-
006
EQ(10) Modelling DLFrance/Belgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant -0.0820533 0.04060 -2.02 0.0446
0.0201
Trend 5.27450e-005 3.517e-005 1.50 0.1353
0.0112
LFrance/Belgium_1 -0.0402793 0.01914 -2.10 0.0366
0.0218
sigma 0.0118449 RSS 0.0279202324
R^2 0.0269562 F(2,199) = 2.756 [0.066]
log-likelihood 610.928 DW 1.23
no. of observations 202 no. of parameters 3
mean(Y) 0.00178439 var(Y) 0.000142048
EQ(11) Modelling DLFrance/Belgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)

9. Coefficient Std.Error t-value t-prob Part.R^2
Constant -0.0255781 0.01521 -1.68 0.0943
0.0139
LFrance/Belgium_1 -0.0140523 0.007802 -1.80 0.0732
0.0160
sigma 0.0118819 RSS 0.0282357082
R^2 0.0159616 F(1,200) = 3.244 [0.073]
log-likelihood 609.793 DW 1.25
no. of observations 202 no. of parameters 2
mean(Y) 0.00178439 var(Y) 0.000142048
EQ(12) Modelling DLFrance/Belgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LFrance/Belgium_1 -0.000956051 0.0004306 -2.22 0.0275
0.0239
sigma 0.0119357 RSS 0.0286347099
log-likelihood 608.376 DW 1.25
no. of observations 202 no. of parameters 1
mean(Y) 0.00178439 var(Y) 0.000142048
EQ(17) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0192151 0.009474 2.03 0.0439
0.0203
Trend 7.54858e-005 7.164e-005 1.05 0.2933
0.0055
LFrance/Germany_1 -0.0251260 0.01782 -1.41 0.1600

10. 0.0099
sigma 0.0125617 RSS 0.0314015384
R^2 0.0213727 F(2,199) = 2.173 [0.117]
log-likelihood 599.06 DW 1.24
no. of observations 202 no. of parameters 3
mean(Y) 0.00370822 var(Y) 0.000158848
EQ(18) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.00998048 0.003598 2.77 0.0061
0.0370
LFrance/Germany_1 -0.00678005 0.003770 -1.80 0.0736
0.0159
sigma 0.0125652 RSS 0.0315767197
R^2 0.0159132 F(1,200) = 3.234 [0.074]
log-likelihood 598.498 DW 1.25
no. of observations 202 no. of parameters 2
mean(Y) 0.00370822 var(Y) 0.000158848
EQ(19) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LFrance/Germany_1 0.00335708 0.0009417 3.57 0.0005
0.0595
sigma 0.0127727 RSS 0.0327915104
log-likelihood 594.686 DW 1.22
no. of observations 202 no. of parameters 1
mean(Y) 0.00370822 var(Y) 0.000158848

11. EQ(20) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0324338 0.03354 0.967 0.3346
0.0047
Trend 1.68881e-005 3.010e-005 0.561 0.5753
0.0016
LBelgium/Germany_1 -0.0112248 0.01269 -0.885 0.3774
0.0039
sigma 0.00785526 RSS 0.0122793188
R^2 0.00780208 F(2,199) = 0.7824 [0.459]
log-likelihood 693.893 DW 1.34
no. of observations 202 no. of parameters 3
mean(Y) 0.00192383 var(Y) 6.12667e-005
EQ(21) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0147556 0.01147 1.29 0.1998
0.0082
LBelgium/Germany_1 -0.00446743 0.003989 -1.12 0.2641
0.0062
sigma 0.00784179 RSS 0.0122987469
R^2 0.00623224 F(1,200) = 1.254 [0.264]
log-likelihood 693.734 DW 1.34
no. of observations 202 no. of parameters 2
mean(Y) 0.00192383 var(Y) 6.12667e-005
EQ(22) Modelling DLBelgium/Germany by OLS

12. The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
LBelgium/Germany_1 0.000657903 0.0001922 3.42
0.0007 0.0551
sigma 0.00785456 RSS 0.0124005016
log-likelihood 692.901 DW 1.34
no. of observations 202 no. of parameters 1
mean(Y) 0.00192383 var(Y) 6.12667e-005
H0 unit root
H1 STATIONARY
ALMOST OF THEM SUGGEST I0
ADF TEST
H0 I(1)
H1 I(2)
EQ(23) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.336949 0.06742 5.00 0.0000
0.1125
LBelgium/Germany_1 -0.0179784 0.01208 -1.49 0.1383
0.0111
Constant 0.0494398 0.03191 1.55 0.1229
0.0120
Trend 3.40206e-005 2.873e-005 1.18 0.2377
0.0071

13. sigma 0.00743136 RSS 0.0108793353
R^2 0.119947 F(3,197) = 8.95 [0.000]**
log-likelihood 702.125 DW 1.82
no. of observations 201 no. of parameters 4
mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(24) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.326982 0.06696 4.88 0.0000
0.1075
LBelgium/Germany_1 -0.00439956 0.003809 -1.16
0.2495 0.0067
Constant 0.0139460 0.01096 1.27 0.2047
0.0081
sigma 0.00743891 RSS 0.0109567886
R^2 0.113682 F(2,198) = 12.7 [0.000]**
log-likelihood 701.412 DW 1.82
no. of observations 201 no. of parameters 3
mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(25) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.329561 0.06703 4.92 0.0000
0.1083
LBelgium/Germany_1 0.000441060 0.0001882 2.34
0.0201 0.0269
sigma 0.00745046 RSS 0.0110463712

14. log-likelihood 700.594 DW 1.82
no. of observations 201 no. of parameters 2
mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(26) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance/Germany_1 0.394828 0.06590 5.99 0.0000
0.1541
Constant 0.0253629 0.008845 2.87 0.0046
0.0401
LFrance/Germany_1 -0.0411394 0.01669 -2.46 0.0146
0.0299
Trend 0.000146035 6.721e-005 2.17 0.0310
0.0234
sigma 0.011599 RSS 0.0265035905
R^2 0.17352 F(3,197) = 13.79 [0.000]**
log-likelihood 612.638 DW 1.94
no. of observations 201 no. of parameters 4
mean(Y) 0.00373002 var(Y) 0.000159542
EQ(27) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance/Germany_1 0.370646 0.06556 5.65 0.0000
0.1390
Constant 0.00761390 0.003423 2.22 0.0273
0.0244
LFrance/Germany_1 -0.00568251 0.003554 -1.60 0.1115
0.0127

15. sigma 0.0117074 RSS 0.0271387011
R^2 0.153715 F(2,198) = 17.98 [0.000]**
log-likelihood 610.258 DW 1.92
no. of observations 201 no. of parameters 3
mean(Y) 0.00373002 var(Y) 0.000159542
EQ(28) Modelling DLFrance/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance/Germany_1 0.390919 0.06556 5.96 0.0000
0.1516
LFrance/Germany_1 0.00196840 0.0009030 2.18 0.0304
0.0233
sigma 0.011823 RSS 0.0278166762
log-likelihood 607.779 DW 1.92
no. of observations 201 no. of parameters 2
mean(Y) 0.00373002 var(Y) 0.000159542
EQ(29) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.336949 0.06742 5.00 0.0000
0.1125
Constant 0.0494398 0.03191 1.55 0.1229
0.0120
Trend 3.40206e-005 2.873e-005 1.18 0.2377
0.0071
LBelgium/Germany_1 -0.0179784 0.01208 -1.49 0.1383
0.0111
sigma 0.00743136 RSS 0.0108793353

16. R^2 0.119947 F(3,197) = 8.95 [0.000]**
log-likelihood 702.125 DW 1.82
no. of observations 201 no. of parameters 4
mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(30) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.326982 0.06696 4.88 0.0000
0.1075
Constant 0.0139460 0.01096 1.27 0.2047
0.0081
LBelgium/Germany_1 -0.00439956 0.003809 -1.16
0.2495 0.0067
sigma 0.00743891 RSS 0.0109567886
R^2 0.113682 F(2,198) = 12.7 [0.000]**
log-likelihood 701.412 DW 1.82
no. of observations 201 no. of parameters 3
mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(31) Modelling DLBelgium/Germany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium/Germany_1 0.329561 0.06703 4.92 0.0000
0.1083
LBelgium/Germany_1 0.000441060 0.0001882 2.34
0.0201 0.0269
sigma 0.00745046 RSS 0.0110463712
log-likelihood 700.594 DW 1.82
no. of observations 201 no. of parameters 2

17. mean(Y) 0.00194223 var(Y) 6.15032e-005
EQ(32) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium_1 0.326990 0.06678 4.90 0.0000
0.1085
Constant 0.0218492 0.01332 1.64 0.1024 0.0135
LBelgium_1 -0.00481865 0.004012 -1.20 0.2312
0.0073
Trend -1.78575e-006 1.997e-005 -0.0894 0.9288
0.0000
sigma 0.00323924 RSS 0.00206705122
R^2 0.366874 F(3,197) = 38.05 [0.000]**
log-likelihood 869.03 DW 2.07
no. of observations 201 no. of parameters 4
mean(DLBelgium) 0.0049045 var(DLBelgium) 1.62429e-
005
EQ(33) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium_1 0.327704 0.06613 4.96 0.0000
0.1103
Constant 0.0229921 0.003726 6.17 0.0000 0.1613
LBelgium_1 -0.00516766 0.0009288 -5.56 0.0000
0.1352
sigma 0.00323111 RSS 0.00206713512
R^2 0.366848 F(2,198) = 57.36 [0.000]**
log-likelihood 869.025 DW 2.07

18. no. of observations 201 no. of parameters 3
mean(DLBelgium) 0.0049045 var(DLBelgium) 1.62429e-
005
EQ(34) Modelling DLBelgium by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLBelgium_1 0.563880 0.05875 9.60 0.0000
0.3165
LBelgium_1 0.000537264 9.763e-005 5.50 0.0000
0.1321
sigma 0.00351932 RSS 0.00246473478
log-likelihood 851.345 DW 2.26
no. of observations 201 no. of parameters 2
mean(DLBelgium) 0.0049045 var(DLBelgium) 1.62429e-
005
EQ(35) Modelling DLFrance by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance_1 0.465581 0.06391 7.28 0.0000 0.2122
Constant -0.00635720 0.006970 -0.912 0.3628
0.0042
LFrance_1 0.00411569 0.002388 1.72 0.0864
0.0148
Trend -5.22226e-005 1.823e-005 -2.86 0.0046 0.0400
sigma 0.00249668 RSS 0.00122797857
R^2 0.57419 F(3,197) = 88.55 [0.000]**
log-likelihood 921.365 DW 2.13
no. of observations 201 no. of parameters 4

19. mean(DLFrance) 0.00670529 var(DLFrance) 1.43476e-005
EQ(36) Modelling DLFrance by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance_1 0.541023 0.05928 9.13 0.0000 0.2961
Constant 0.0125788 0.002251 5.59 0.0000 0.1363
LFrance_1 -0.00256031 0.0005327 -4.81 0.0000
0.1045
sigma 0.00254171 RSS 0.00127913695
R^2 0.556451 F(2,198) = 124.2 [0.000]**
log-likelihood 917.263 DW 2.2
no. of observations 201 no. of parameters 3
mean(DLFrance) 0.00670529 var(DLFrance) 1.43476e-005
EQ(37) Modelling DLFrance by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLFrance_1 0.774790 0.04509 17.2 0.0000 0.5974
LFrance_1 0.000377414 9.312e-005 4.05 0.0001
0.0763
sigma 0.00272799 RSS 0.00148094365
log-likelihood 902.541 DW 2.45
no. of observations 201 no. of parameters 2
mean(DLFrance) 0.00670529 var(DLFrance) 1.43476e-005
EQ(38) Modelling DLGermany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)

20. Coefficient Std.Error t-value t-prob Part.R^2
DLGermany_1 0.365669 0.06631 5.51 0.0000
0.1337
Constant 0.0197762 0.01776 1.11 0.2667 0.0063
LGermany_1 -0.00453649 0.004816 -0.942 0.3474
0.0045
Trend 9.17538e-007 1.418e-005 0.0647 0.9485
0.0000
sigma 0.00266156 RSS 0.00139552576
R^2 0.254234 F(3,197) = 22.39 [0.000]**
log-likelihood 908.511 DW 2.03
no. of observations 201 no. of parameters 4
mean(DLGermany) 0.00287059 var(DLGermany) 9.30977e-
006
EQ(39) Modelling DLGermany by OLS
The dataset is: new09.in7
The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLGermany_1 0.365186 0.06572 5.56 0.0000
0.1349
Constant 0.0186701 0.004802 3.89 0.0001 0.0709
LGermany_1 -0.00423450 0.001187 -3.57 0.0005
0.0604
sigma 0.00265486 RSS 0.00139555543
R^2 0.254218 F(2,198) = 33.75 [0.000]**
log-likelihood 908.509 DW 2.03
no. of observations 201 no. of parameters 3
mean(DLGermany) 0.00287059 var(DLGermany) 9.30977e-
006
EQ(40) Modelling DLGermany by OLS
The dataset is: new09.in7

21. The estimation sample is: 1973(6) - 1990(2)
Coefficient Std.Error t-value t-prob Part.R^2
DLGermany_1 0.468260 0.06223 7.52 0.0000
0.2215
LGermany_1 0.000374458 6.579e-005 5.69 0.0000
0.1400
sigma 0.00274739 RSS 0.00150208012
log-likelihood 901.116 DW 2.11
no. of observations 201 no. of parameters 2
mean(DLGermany) 0.00287059 var(DLGermany) 9.30977e-
006
Unit-root tests
The dataset is: new09.in7
The sample is: 1974(5) - 1990(2)
LFrance: ADF tests (T=190, Constant; 5%=-2.88 1%=-3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC
F-prob
12 -1.357 0.99925 0.002062 3.358 0.0010 -12.30
11 -1.542 0.99913 0.002121 0.04993 0.9602 -12.25
0.0010
10 -1.553 0.99912 0.002115 0.7887 0.4314 -12.26
0.0042
9 -1.613 0.99909 0.002112 1.623 0.1063 -12.26
0.0090
8 -1.762 0.99901 0.002122 0.03910 0.9689 -12.26
0.0067
7 -1.782 0.99901 0.002116 -1.004 0.3165 -12.27
0.0142
6 -1.693 0.99906 0.002116 4.666 0.0000 -12.28
0.0183
5 -2.310 0.99866 0.002233 2.328 0.0210 -12.17
0.0000

22. 4 -2.774 0.99840 0.002260 -2.795 0.0057 -12.15
0.0000
3 -2.300 0.99867 0.002301 5.080 0.0000 -12.12
0.0000
2 -3.405* 0.99797 0.002450 2.586 0.0105 -12.00
0.0000
1 -4.317** 0.99751 0.002487 9.193 0.0000 -11.98
0.0000
0 -10.13** 0.99434 0.002988 -11.62
0.0000
LBelgium: ADF tests (T=190, Constant; 5%=-2.88 1%=-3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC
F-prob
12 -1.597 0.99792 0.003028 3.324 0.0011 -11.53
11 -1.894 0.99747 0.003112 -0.2390 0.8114 -11.48
0.0011
10 -1.884 0.99751 0.003104 -0.7801 0.4364 -11.49
0.0046
9 -1.817 0.99761 0.003101 1.347 0.1798 -11.50
0.0097
8 -2.001 0.99739 0.003108 1.148 0.2525 -11.50
0.0103
7 -2.202 0.99715 0.003111 -0.7425 0.4588 -11.50
0.0125
6 -2.115 0.99730 0.003107 1.692 0.0924 -11.51
0.0193
5 -2.457 0.99691 0.003122 2.009 0.0460 -11.50
0.0122
4 -2.943* 0.99635 0.003148 3.500 0.0006 -11.49
0.0051
3 -3.999** 0.99511 0.003242 0.9936 0.3217 -11.44
0.0001
2 -4.581** 0.99471 0.003242 0.9753 0.3307 -11.44
0.0001
1 -5.312** 0.99430 0.003242 4.105 0.0001 -11.45

23. 0.0002
0 -8.407** 0.99199 0.003376 -11.37
0.0000
LGermany: ADF tests (T=190, Constant; 5%=-2.88 1%=-3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC
F-prob
12 -0.9617 0.99863 0.002338 3.426 0.0008 -12.05
11 -1.337 0.99805 0.002408 3.889 0.0001 -11.99
0.0008
10 -1.903 0.99715 0.002502 0.7668 0.4442 -11.92
0.0000
9 -2.039 0.99698 0.002499 1.961 0.0514 -11.93
0.0000
8 -2.395 0.99648 0.002518 1.040 0.2996 -11.92
0.0000
7 -2.650 0.99618 0.002519 1.808 0.0723 -11.92
0.0000
6 -3.180* 0.99554 0.002535 -2.974 0.0033 -11.91
0.0000
5 -2.549 0.99643 0.002588 -0.3619 0.7179 -11.88
0.0000
4 -2.535 0.99654 0.002582 -0.8986 0.3700 -11.89
0.0000
3 -2.411 0.99677 0.002581 1.527 0.1286 -11.89
0.0000
2 -2.785 0.99634 0.002590 0.9681 0.3343 -11.89
0.0000
1 -3.062* 0.99607 0.002590 5.313 0.0000 -11.90
0.0000
0 -4.730** 0.99385 0.002771 -11.77
0.0000
LFrance/Belgium: ADF tests (T=190, Constant; 5%=-2.88 1%=-
3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC

24. F-prob
12 -1.110 0.99116 0.01047 -0.8751 0.3827 -9.048
11 -1.126 0.99105 0.01046 -1.072 0.2852 -9.054
0.3827
10 -1.142 0.99092 0.01047 -2.186 0.0301 -9.058
0.3861
9 -1.188 0.99045 0.01058 1.229 0.2208 -9.042
0.0864
8 -1.165 0.99063 0.01059 2.479 0.0141 -9.044
0.0884
7 -1.143 0.99068 0.01074 0.3712 0.7109 -9.021
0.0152
6 -1.144 0.99069 0.01072 -0.2431 0.8082 -9.031
0.0270
5 -1.149 0.99067 0.01069 -1.023 0.3075 -9.041
0.0454
4 -1.158 0.99060 0.01069 -0.8568 0.3926 -9.046
0.0517
3 -1.161 0.99058 0.01068 -2.119 0.0355 -9.052
0.0636
2 -1.226 0.98997 0.01078 -0.9129 0.3625 -9.039
0.0247
1 -1.289 0.98948 0.01078 5.761 0.0000 -9.045
0.0296
0 -1.090 0.99037 0.01166 -8.892
0.0000
LFrance/Germany: ADF tests (T=190, Constant; 5%=-2.88 1%=-
3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC
F-prob
12 -0.6070 0.99789 0.01055 -2.396 0.0176 -9.033
11 -0.5990 0.99789 0.01069 -1.805 0.0728 -9.011
0.0176
10 -0.5818 0.99794 0.01076 -0.3928 0.6949 -9.003
0.0119

25. 9 -0.5804 0.99795 0.01073 1.063 0.2891 -9.013
0.0288
8 -0.5674 0.99800 0.01073 2.019 0.0450 -9.017
0.0376
7 -0.5464 0.99805 0.01083 2.034 0.0434 -9.005
0.0145
6 -0.5394 0.99806 0.01092 0.1321 0.8950 -8.993
0.0057
5 -0.5412 0.99806 0.01089 -0.6065 0.5449 -9.004
0.0107
4 -0.5307 0.99810 0.01087 -0.7124 0.4771 -9.012
0.0165
3 -0.5201 0.99814 0.01086 -0.9540 0.3413 -9.020
0.0231
2 -0.5204 0.99814 0.01085 -0.5035 0.6152 -9.026
0.0274
1 -0.5291 0.99812 0.01083 5.395 0.0000 -9.035
0.0390
0 -0.5403 0.99794 0.01161 -8.901
0.0000
LBelgium/Germany: ADF tests (T=190, Constant; 5%=-2.88
1%=-3.47)
D-lag t-adf beta Y_1 sigma t-DY_lag t-prob AIC
F-prob
12 -0.6166 0.99782 0.006538 0.5495 0.5834 -9.990
11 -0.6083 0.99785 0.006525 -1.173 0.2423 -9.998
0.5834
10 -0.6252 0.99779 0.006532 -1.808 0.0722 -10.00
0.4350
9 -0.6861 0.99756 0.006573 0.9361 0.3505 -9.993
0.1806
8 -0.6261 0.99778 0.006571 0.6478 0.5180 -9.999
0.2177
7 -0.5868 0.99793 0.006560 1.005 0.3160 -10.01
0.2881

26. 6 -0.5306 0.99813 0.006560 -0.2897 0.7724 -10.01
0.3028
5 -0.5494 0.99807 0.006544 1.481 0.1402 -10.02
0.3982
4 -0.4962 0.99825 0.006565 1.109 0.2690 -10.02
0.3054
3 -0.4448 0.99843 0.006569 1.607 0.1097 -10.02
0.2985
2 -0.3763 0.99867 0.006597 -1.197 0.2328 -10.02
0.2126
1 -0.4202 0.99852 0.006605 4.826 0.0000 -10.02
0.2005
0 -0.2665 0.99900 0.006985 -9.917
0.0003
(3) 黄色部分是重要的数据
SYS( 1) Estimating the system by OLS
The dataset is: new09.in7
The estimation sample is: 1974(4) - 1990(2)
URF equation for: LFrance/Belgium
Coefficient Std.Error t-value t-prob
LFrance/Belgium_1 1.27793 0.07985 16.0 0.0000
LFrance/Belgium_2 -0.309790 0.1287 -2.41 0.0172

27. LFrance/Belgium_3 -0.135067 0.1286 -1.05 0.2954
LFrance/Belgium_4 0.0602494 0.1277 0.472 0.6377
LFrance/Belgium_5 -0.0144114 0.1285 -0.112 0.9109
LFrance/Belgium_6 -0.00309561 0.1268 -0.0244 0.9806
LFrance/Belgium_7 0.0294940 0.1275 0.231 0.8174
LFrance/Belgium_8 0.162431 0.1272 1.28 0.2037
LFrance/Belgium_9 -0.0270322 0.1271 -0.213 0.8319
LFrance/Belgium_10 -0.267770 0.1229 -2.18 0.0309
LFrance/Belgium_11 0.111255 0.1227 0.906 0.3661
LFrance/Belgium_12 -0.00155779 0.07546 -0.0206 0.9836
LFrance_1 0.385940 0.4200 0.919 0.3596
LFrance_2 -1.31872 0.7486 -1.76 0.0801
LFrance_3 1.97146 0.7607 2.59 0.0105
LFrance_4 -1.04391 0.7477 -1.40 0.1647
LFrance_5 0.324587 0.7649 0.424 0.6719
LFrance_6 -0.567520 0.7572 -0.750 0.4547
LFrance_7 0.460296 0.7576 0.608 0.5444
LFrance_8 -0.100251 0.7546 -0.133 0.8945
LFrance_9 -0.223160 0.7339 -0.304 0.7615
LFrance_10 0.760773 0.7369 1.03 0.3035
LFrance_11 -1.23509 0.7159 -1.73 0.0865
LFrance_12 0.597129 0.4041 1.48 0.1416
LBelgium_1 -0.0722244 0.2914 -0.248 0.8046
LBelgium_2 0.337063 0.4337 0.777 0.4382
LBelgium_3 -0.410626 0.4445 -0.924 0.3570
LBelgium_4 -0.450874 0.4508 -1.00 0.3188
LBelgium_5 0.432919 0.4426 0.978 0.3295
LBelgium_6 -0.191279 0.4382 -0.437 0.6631
LBelgium_7 0.115131 0.4390 0.262 0.7935
LBelgium_8 -0.250199 0.4402 -0.568 0.5706
LBelgium_9 0.637659 0.4348 1.47 0.1445
LBelgium_10 -0.503691 0.4372 -1.15 0.2511
LBelgium_11 0.479278 0.4390 1.09 0.2766
LBelgium_12 -0.111923 0.2770 -0.404 0.6867
Constant -0.307948 0.1164 -2.65 0.0090

28. sigma = 0.0101403 RSS = 0.01583507807
URF equation for: LFrance
Coefficient Std.Error t-value t-prob
LFrance/Belgium_1 0.0104870 0.01579 0.664 0.5075
LFrance/Belgium_2 -0.0111617 0.02544 -0.439 0.6614
LFrance/Belgium_3 -0.0237979 0.02544 -0.936 0.3509
LFrance/Belgium_4 0.0589219 0.02525 2.33 0.0209
LFrance/Belgium_5 -0.00695515 0.02541 -0.274 0.7847
LFrance/Belgium_6 -0.0373424 0.02508 -1.49 0.1385
LFrance/Belgium_7 0.0230060 0.02521 0.912 0.3630
LFrance/Belgium_8 -0.0271489 0.02516 -1.08 0.2822
LFrance/Belgium_9 0.0329476 0.02514 1.31 0.1919
LFrance/Belgium_10 -0.0419706 0.02430 -1.73 0.0862
LFrance/Belgium_11 0.0288738 0.02427 1.19 0.2360
LFrance/Belgium_12 -0.00523507 0.01492 -0.351 0.7262
LFrance_1 1.47084 0.08304 17.7 0.0000
LFrance_2 -0.493216 0.1480 -3.33 0.0011
LFrance_3 0.361839 0.1504 2.41 0.0173
LFrance_4 -0.638682 0.1478 -4.32 0.0000
LFrance_5 0.316810 0.1512 2.09 0.0378
LFrance_6 0.290642 0.1497 1.94 0.0540
LFrance_7 -0.320522 0.1498 -2.14 0.0339
LFrance_8 -0.0522679 0.1492 -0.350 0.7266
LFrance_9 0.0848384 0.1451 0.585 0.5596
LFrance_10 0.150978 0.1457 1.04 0.3017
LFrance_11 -0.118942 0.1415 -0.840 0.4020
LFrance_12 -0.0425372 0.07991 -0.532 0.5953
LBelgium_1 -0.103993 0.05762 -1.80 0.0730
LBelgium_2 0.205379 0.08574 2.40 0.0178
LBelgium_3 -0.254146 0.08788 -2.89 0.0044
LBelgium_4 0.0752933 0.08913 0.845 0.3995
LBelgium_5 0.0359132 0.08750 0.410 0.6821
LBelgium_6 0.110359 0.08664 1.27 0.2047
LBelgium_7 -0.131423 0.08680 -1.51 0.1320
LBelgium_8 0.0330297 0.08703 0.380 0.7048

29. LBelgium_9 0.0910438 0.08597 1.06 0.2912
LBelgium_10 -0.224310 0.08645 -2.59 0.0104
LBelgium_11 0.124484 0.08679 1.43 0.1535
LBelgium_12 0.0203587 0.05477 0.372 0.7106
Constant 0.0354463 0.02301 1.54 0.1255
sigma = 0.00200488 RSS = 0.0006190098657
URF equation for: LBelgium
Coefficient Std.Error t-value t-prob
LFrance/Belgium_1 0.00357489 0.02257 0.158 0.8743
LFrance/Belgium_2 -0.0126261 0.03636 -0.347 0.7289
LFrance/Belgium_3 -0.00383292 0.03636 -0.105 0.9162
LFrance/Belgium_4 0.0264039 0.03609 0.732 0.4655
LFrance/Belgium_5 -0.0208393 0.03632 -0.574 0.5670
LFrance/Belgium_6 -0.00161438 0.03585 -0.0450 0.9641
LFrance/Belgium_7 -0.0247817 0.03604 -0.688 0.4927
LFrance/Belgium_8 0.0423463 0.03596 1.18 0.2408
LFrance/Belgium_9 -0.00238368 0.03593 -0.0663 0.9472
LFrance/Belgium_10 -0.0369844 0.03474 -1.06 0.2887
LFrance/Belgium_11 0.0293605 0.03469 0.846 0.3986
LFrance/Belgium_12 -0.0180046 0.02133 -0.844 0.3998
LFrance_1 -0.0995052 0.1187 -0.838 0.4032
LFrance_2 0.165785 0.2116 0.784 0.4345
LFrance_3 0.101434 0.2150 0.472 0.6377
LFrance_4 -0.177123 0.2113 -0.838 0.4032
LFrance_5 0.0245123 0.2162 0.113 0.9099
LFrance_6 0.340829 0.2140 1.59 0.1133
LFrance_7 -0.374297 0.2141 -1.75 0.0824
LFrance_8 -0.0700255 0.2133 -0.328 0.7431
LFrance_9 0.177214 0.2074 0.854 0.3942
LFrance_10 0.180473 0.2082 0.867 0.3875
LFrance_11 -0.394862 0.2023 -1.95 0.0528
LFrance_12 0.173936 0.1142 1.52 0.1298
LBelgium_1 1.06640 0.08235 12.9 0.0000
LBelgium_2 -0.160496 0.1226 -1.31 0.1923

30. LBelgium_3 -0.178947 0.1256 -1.42 0.1563
LBelgium_4 0.305609 0.1274 2.40 0.0176
LBelgium_5 -0.0198356 0.1251 -0.159 0.8742
LBelgium_6 -0.126473 0.1238 -1.02 0.3087
LBelgium_7 -0.0291057 0.1241 -0.235 0.8148
LBelgium_8 0.151122 0.1244 1.21 0.2263
LBelgium_9 -0.0326786 0.1229 -0.266 0.7906
LBelgium_10 -0.0869635 0.1236 -0.704 0.4826
LBelgium_11 0.0450370 0.1241 0.363 0.7171
LBelgium_12 -0.00605258 0.07829 -0.0773 0.9385
Constant 0.0622459 0.03289 1.89 0.0603
sigma = 0.00286568 RSS = 0.001264666523
log-likelihood 2436.99964 -T/2log|Omega| 3250.05141
|Omega| 1.6600113e-015 log|Y'Y/T| -6.84461615
R^2(LR) 1 R^2(LM) 0.990616
no. of observations 191 no. of parameters 111
F-test on regressors except unrestricted: F(111,456) = 35967.7
[0.0000] **
F-tests on retained regressors, F(3,152) =
LFrance/Belgium_1 84.5353 [0.000]**LFrance/Belgium_2
1.98731 [0.118]
LFrance/Belgium_3 0.620620 [0.603] LFrance/Belgium_4
1.84291 [0.142]
LFrance/Belgium_5 0.119660 [0.948] LFrance/Belgium_6
0.767952 [0.514]
LFrance/Belgium_7 0.572443 [0.634] LFrance/Belgium_8
1.77795 [0.154]
LFrance/Belgium_9 0.649431 [0.584] LFrance/Belgium_10
2.61722 [0.053]
LFrance/Belgium_11 0.826255 [0.481] LFrance/Belgium_12
0.242228 [0.867]
LFrance_1 112.831 [0.000]** LFrance_2 5.30298
[0.002]**

31. LFrance_3 3.91118 [0.010]* LFrance_4 6.60333
[0.000]**
LFrance_5 1.52990 [0.209] LFrance_6 1.87779
[0.136]
LFrance_7 2.16555 [0.094] LFrance_8 0.0662745
[0.978]
LFrance_9 0.317530 [0.813] LFrance_10 0.823492
[0.483]
LFrance_11 2.34789 [0.075] LFrance_12 1.90022
[0.132]
LBelgium_1 64.1130 [0.000]** LBelgium_2 3.25593
[0.023]*
LBelgium_3 3.14657 [0.027]* LBelgium_4 2.19467
[0.091]
LBelgium_5 0.372815 [0.773] LBelgium_6 1.27165
[0.286]
LBelgium_7 0.801519 [0.495] LBelgium_8 0.578631
[0.630]
LBelgium_9 1.09842 [0.352] LBelgium_10 2.56105
[0.057]
LBelgium_11 1.01961 [0.386] LBelgium_12 0.117583
[0.950]
Constant 3.88549 [0.010]*
correlation of URF residuals (standard deviations on diagonal)
LFrance/Belgium LFrance LBelgium
LFrance/Belgium 0.010140 0.051944 -0.040747
LFrance 0.051944 0.0020049 0.24802
LBelgium -0.040747 0.24802 0.0028657
correlation between actual and fitted
LFrance/Belgium LFrance LBelgium
0.99549 0.99999 0.99995
I(1) cointegration analysis, 1974(4) - 1990(2)
eigenvalue loglik for rank
2409.911 0

32. 0.15264 2425.728 1
0.081940 2433.893 2
0.032007 2437.000 3
H0:rank<= Trace test [ Prob]
0 54.177 [0.000] **
1 22.542 [0.022] *
2 6.2133 [0.181]
Asymptotic p-values based on: Restricted constant
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta (scaled on diagonal; cointegrating vectors in columns)
LFrance/Belgium 1.0000 0.80740 -5.6671
LFrance -1.2433 1.0000 1.7194
LBelgium 1.7382 -1.8156 1.0000
Constant -0.18262 4.8069 -22.299
alpha
LFrance/Belgium -0.064213 -0.067818 -0.00028364
LFrance -0.0069044 0.0027978 -0.00092994
LBelgium -0.028709 0.012456 0.00012874
long-run matrix, rank 3
LFrance/Belgium LFrance LBelgium
Constant
LFrance/Belgium -0.11736 0.011531 0.011234 -
0.30795
LFrance 0.00062463 0.0097832 -0.018011
0.035446
LBelgium -0.019382 0.048371 -0.072388
0.062246

33. // Batch code for SYS( 1)
module("PcGive");
package("PcGive", "Multiple-equation");
usedata("new09.in7");
system
{
Y = "LFrance/Belgium", LFrance, LBelgium;
Z = Constant, "LFrance/Belgium_1", "LFrance/Belgium_2",
"LFrance/Belgium_3", "LFrance/Belgium_4",
"LFrance/Belgium_5",
"LFrance/Belgium_6", "LFrance/Belgium_7",
"LFrance/Belgium_8",
"LFrance/Belgium_9", "LFrance/Belgium_10",
"LFrance/Belgium_11",
"LFrance/Belgium_12", LFrance_1, LFrance_2,
LFrance_3,
LFrance_4, LFrance_5, LFrance_6, LFrance_7, LFrance_8,
LFrance_9, LFrance_10, LFrance_11, LFrance_12,
LBelgium_1,
LBelgium_2, LBelgium_3, LBelgium_4, LBelgium_5,
LBelgium_6,
LBelgium_7, LBelgium_8, LBelgium_9, LBelgium_10,
LBelgium_11,
LBelgium_12;
}
estimate("OLS", 1974, 4, 1990, 2);
dynamics();
SYS( 2) Cointegrated VAR
The dataset is: new09.in7
The estimation sample is: 1974(4) - 1990(2)
Cointegrated VAR (12) in:
[0] = LFrance/Belgium

34. [1] = LFrance
[2] = LBelgium
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta
LFrance/Belgium 1.0000
LFrance -1.2433
LBelgium 1.7382
Constant -0.18262
alpha
LFrance/Belgium -0.064213
LFrance -0.0069044
LBelgium -0.028709
Standard errors of alpha
LFrance/Belgium 0.023864
LFrance 0.0046458
LBelgium 0.0066255
Restricted long-run matrix, rank 1
LFrance/Belgium LFrance LBelgium
Constant
LFrance/Belgium -0.064213 0.079837 -0.11162
0.011726
LFrance -0.0069044 0.0085843 -0.012001
0.0012609
LBelgium -0.028709 0.035694 -0.049902
0.0052427
Standard errors of long-run matrix
LFrance/Belgium 0.023864 0.029670 0.041480
0.0043579
LFrance 0.0046458 0.0057762 0.0080753

35. 0.00084840
LBelgium 0.0066255 0.0082376 0.011517
0.0012099
Reduced form beta
LFrance/Belgium -1.0000
LFrance 1.2433
LBelgium -1.7382
Constant 0.18262
Standard errors of reduced form beta
LFrance/Belgium 0.00000
LFrance 0.28616
LBelgium 0.45912
Constant 0.72170
Moving-average impact matrix
0.96145 4.6128 -3.2599
1.7958 37.208 -12.965
0.73138 23.960 -7.3983
log-likelihood 2425.72842 -T/2log|Omega| 3238.7802
no. of observations 191 no. of parameters 105
rank of long-run matrix 1 no. long-run restrictions 0
beta is not identified
No restrictions imposed
LFrance/Belgium: Portmanteau(12): 1.48753
LFrance : Portmanteau(12): 8.94026
LBelgium : Portmanteau(12): 8.36552
LFrance/Belgium: Normality test: Chi^2(2) = 38.144
[0.0000]**
LFrance : Normality test: Chi^2(2) = 22.000 [0.0000]**
LBelgium : Normality test: Chi^2(2) = 2.9930 [0.2239]
LFrance/Belgium: ARCH 1-7 test: F(7,142) = 3.9842
[0.0005]**

36. LFrance : ARCH 1-7 test: F(7,142) = 0.28833 [0.9576]
LBelgium : ARCH 1-7 test: F(7,142) = 0.62275 [0.7365]
LFrance/Belgium: Hetero test: F(72,81) = 0.91774 [0.6438]
LFrance : Hetero test: F(72,81) = 0.50705 [0.9982]
LBelgium : Hetero test: F(72,81) = 0.51161 [0.9979]
Vector Portmanteau(12): 45.4787
Vector Normality test: Chi^2(6) = 61.569 [0.0000]**
Vector Hetero test: F(432,463)= 0.81429 [0.9848]
SYS( 3) Estimating the system by OLS
The dataset is: new09.in7
The estimation sample is: 1974(4) - 1990(2)
URF equation for: LFrance/Germany
Coefficient Std.Error t-value t-prob
LFrance/Germany_1 1.18243 0.08104 14.6 0.0000
LFrance/Germany_2 -0.254381 0.1257 -2.02 0.0447
LFrance/Germany_3 -0.0111361 0.1263 -0.0882 0.9299
LFrance/Germany_4 0.0268588 0.1254 0.214 0.8307
LFrance/Germany_5 -0.0811245 0.1244 -0.652 0.5153
LFrance/Germany_6 0.0385568 0.1183 0.326 0.7450
LFrance/Germany_7 0.138214 0.1182 1.17 0.2442
LFrance/Germany_8 -0.0552427 0.1194 -0.463 0.6442
LFrance/Germany_9 0.0907171 0.1157 0.784 0.4344
LFrance/Germany_10 -0.0938167 0.1118 -0.839 0.4028
LFrance/Germany_11 -0.105044 0.1098 -0.957 0.3401
LFrance/Germany_12 0.00748530 0.07084 0.106 0.9160
LFrance_1 0.568700 0.3908 1.46 0.1476
LFrance_2 -1.66185 0.6607 -2.52 0.0129
LFrance_3 2.12237 0.6768 3.14 0.0021
LFrance_4 -1.31341 0.6667 -1.97 0.0506
LFrance_5 0.906003 0.6936 1.31 0.1935
LFrance_6 -1.40503 0.6899 -2.04 0.0434
LFrance_7 1.08005 0.6955 1.55 0.1225
LFrance_8 -0.128726 0.6988 -0.184 0.8541

37. LFrance_9 -0.665868 0.6794 -0.980 0.3286
LFrance_10 0.497608 0.6871 0.724 0.4701
LFrance_11 -0.330165 0.6828 -0.484 0.6294
LFrance_12 0.384502 0.3981 0.966 0.3356
LGermany_1 -0.399822 0.3462 -1.15 0.2500
LGermany_2 0.428888 0.5277 0.813 0.4176
LGermany_3 -0.113032 0.5192 -0.218 0.8279
LGermany_4 -0.306531 0.5163 -0.594 0.5536
LGermany_5 0.349434 0.5177 0.675 0.5007
LGermany_6 0.475014 0.5024 0.945 0.3459
LGermany_7 -1.39212 0.5044 -2.76 0.0065
LGermany_8 0.817985 0.5289 1.55 0.1240
LGermany_9 0.545546 0.5297 1.03 0.3046
LGermany_10 -0.227258 0.5266 -0.432 0.6666
LGermany_11 0.284420 0.5199 0.547 0.5851
LGermany_12 -0.450999 0.3254 -1.39 0.1677
Constant -0.131695 0.2478 -0.531 0.5959
sigma = 0.00994372 RSS = 0.01522714336
URF equation for: LFrance
Coefficient Std.Error t-value t-prob
LFrance/Germany_1 0.00237054 0.01727 0.137 0.8910
LFrance/Germany_2 -0.0222292 0.02678 -0.830 0.4079
LFrance/Germany_3 0.0109498 0.02691 0.407 0.6847
LFrance/Germany_4 0.0263148 0.02672 0.985 0.3263
LFrance/Germany_5 0.0127706 0.02651 0.482 0.6306
LFrance/Germany_6 -0.0559919 0.02521 -2.22 0.0278
LFrance/Germany_7 0.0377117 0.02519 1.50 0.1365
LFrance/Germany_8 -0.0132246 0.02544 -0.520 0.6039
LFrance/Germany_9 0.0120699 0.02466 0.489 0.6252
LFrance/Germany_10 -0.0146932 0.02383 -0.617 0.5384
LFrance/Germany_11 -0.00135161 0.02339 -0.0578 0.9540
LFrance/Germany_12 0.00345209 0.01509 0.229 0.8194
LFrance_1 1.39022 0.08326 16.7 0.0000
LFrance_2 -0.322240 0.1408 -2.29 0.0234

38. LFrance_3 0.167007 0.1442 1.16 0.2486
LFrance_4 -0.556010 0.1421 -3.91 0.0001
LFrance_5 0.372277 0.1478 2.52 0.0128
LFrance_6 0.308417 0.1470 2.10 0.0375
LFrance_7 -0.399356 0.1482 -2.69 0.0078
LFrance_8 -0.0658622 0.1489 -0.442 0.6589
LFrance_9 0.193218 0.1448 1.33 0.1840
LFrance_10 -0.0535239 0.1464 -0.366 0.7152
LFrance_11 -0.0500518 0.1455 -0.344 0.7313
LFrance_12 0.0131828 0.08482 0.155 0.8767
LGermany_1 0.0410234 0.07377 0.556 0.5790
LGermany_2 -0.00344278 0.1124 -0.0306 0.9756
LGermany_3 0.0141478 0.1106 0.128 0.8984
LGermany_4 0.0697912 0.1100 0.634 0.5268
LGermany_5 -0.137718 0.1103 -1.25 0.2138
LGermany_6 0.0525577 0.1071 0.491 0.6242
LGermany_7 -0.0388818 0.1075 -0.362 0.7180
LGermany_8 0.00803967 0.1127 0.0713 0.9432
LGermany_9 -0.0590020 0.1129 -0.523 0.6019
LGermany_10 0.0424012 0.1122 0.378 0.7060
LGermany_11 -0.0357749 0.1108 -0.323 0.7472
LGermany_12 0.0536652 0.06932 0.774 0.4401
Constant -0.0141731 0.05281 -0.268 0.7888
sigma = 0.00211877 RSS = 0.0006913324248
URF equation for: LGermany
Coefficient Std.Error t-value t-prob
LFrance/Germany_1 -0.00995883 0.01876 -0.531 0.5962
LFrance/Germany_2 0.00806314 0.02909 0.277 0.7820
LFrance/Germany_3 0.0364057 0.02923 1.25 0.2149
LFrance/Germany_4 -0.0432459 0.02903 -1.49 0.1383
LFrance/Germany_5 0.00823761 0.02879 0.286 0.7752
LFrance/Germany_6 -0.00739354 0.02738 -0.270 0.7875
LFrance/Germany_7 -0.000402614 0.02737 -0.0147 0.9883
LFrance/Germany_8 0.00640793 0.02763 0.232 0.8169

39. LFrance/Germany_9 -0.0113554 0.02679 -0.424 0.6722
LFrance/Germany_10 0.00921922 0.02588 0.356 0.7222
LFrance/Germany_11 0.00209335 0.02541 0.0824 0.9344
LFrance/Germany_12 -0.00116559 0.01640 -0.0711 0.9434
LFrance_1 0.116560 0.09044 1.29 0.1994
LFrance_2 -0.0817372 0.1529 -0.535 0.5937
LFrance_3 0.0121145 0.1566 0.0773 0.9385
LFrance_4 0.0130135 0.1543 0.0843 0.9329
LFrance_5 -0.117251 0.1605 -0.730 0.4663
LFrance_6 0.157006 0.1597 0.983 0.3270
LFrance_7 -0.109813 0.1610 -0.682 0.4961
LFrance_8 0.0848636 0.1617 0.525 0.6006
LFrance_9 0.267655 0.1573 1.70 0.0908
LFrance_10 -0.349672 0.1590 -2.20 0.0294
LFrance_11 0.0257251 0.1580 0.163 0.8709
LFrance_12 0.0127173 0.09213 0.138 0.8904
LGermany_1 1.16865 0.08013 14.6 0.0000
LGermany_2 -0.244820 0.1221 -2.00 0.0468
LGermany_3 0.118195 0.1202 0.984 0.3269
LGermany_4 -0.108472 0.1195 -0.908 0.3655
LGermany_5 0.0930923 0.1198 0.777 0.4384
LGermany_6 -0.404054 0.1163 -3.47 0.0007
LGermany_7 0.393746 0.1167 3.37 0.0009
LGermany_8 -0.144701 0.1224 -1.18 0.2390
LGermany_9 0.0697007 0.1226 0.569 0.5705
LGermany_10 -0.00537249 0.1219 -0.0441 0.9649
LGermany_11 0.211525 0.1203 1.76 0.0807
LGermany_12 -0.219975 0.07530 -2.92 0.0040
Constant 0.174402 0.05736 3.04 0.0028
sigma = 0.00230147 RSS = 0.0008156992738
log-likelihood 2474.65444 -T/2log|Omega| 3287.70622
|Omega| 1.11910951e-015 log|Y'Y/T| -6.29263643
R^2(LR) 1 R^2(LM) 0.986345
no. of observations 191 no. of parameters 111

40. F-test on regressors except unrestricted: F(111,456) = 49332.7
[0.0000] **
F-tests on retained regressors, F(3,152) =
LFrance/Germany_1 72.3906 [0.000]**LFrance/Germany_2
1.56110 [0.201]
LFrance/Germany_3 0.530140 [0.662] LFrance/Germany_4
1.39341 [0.247]
LFrance/Germany_5 0.271015 [0.846] LFrance/Germany_6
1.80232 [0.149]
LFrance/Germany_7 1.10053 [0.351] LFrance/Germany_8
0.190291 [0.903]
LFrance/Germany_9 0.369824 [0.775] LFrance/Germany_10
0.419550 [0.739]
LFrance/Germany_11 0.312637 [0.816]
LFrance/Germany_12 0.0250941 [0.995]
LFrance_1 95.1567 [0.000]** LFrance_2 3.29445
[0.022]*
LFrance_3 3.43553 [0.019]* LFrance_4 6.12358
[0.001]**
LFrance_5 3.07888 [0.029]* LFrance_6 3.47117
[0.018]*
LFrance_7 3.72339 [0.013]* LFrance_8 0.215050
[0.886]
LFrance_9 1.79252 [0.151] LFrance_10 1.88604
[0.134]
LFrance_11 0.127775 [0.944] LFrance_12 0.307600
[0.820]
LGermany_1 75.0178 [0.000]** LGermany_2 1.70258
[0.169]
LGermany_3 0.353433 [0.787] LGermany_4 0.668355
[0.573]
LGermany_5 1.15449 [0.329] LGermany_6 5.03881
[0.002]**
LGermany_7 7.14852 [0.000]** LGermany_8 1.38611
[0.249]

41. LGermany_9 0.651169 [0.583] LGermany_10
0.133081 [0.940]
LGermany_11 1.30487 [0.275] LGermany_12 4.20461
[0.007]**
Constant 3.57993 [0.015]*
correlation of URF residuals (standard deviations on diagonal)
LFrance/Germany LFrance LGermany
LFrance/Germany 0.0099437 0.15995 0.098497
LFrance 0.15995 0.0021188 0.25420
LGermany 0.098497 0.25420 0.0023015
correlation between actual and fitted
LFrance/Germany LFrance LGermany
0.99918 0.99999 0.99991
I(1) cointegration analysis, 1974(4) - 1990(2)
eigenvalue loglik for rank
2451.615 0
0.15287 2467.458 1
0.056413 2473.003 2
0.017142 2474.654 3
H0:rank<= Trace test [ Prob]
0 46.080 [0.002] **
1 14.393 [0.269]
2 3.3025 [0.536]
Asymptotic p-values based on: Restricted constant
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta (scaled on diagonal; cointegrating vectors in columns)
LFrance/Germany 1.0000 -0.33556 0.052729
LFrance 0.044039 1.0000 -0.31341
LGermany -1.3365 -2.0026 1.0000

42. Constant 4.1392 4.5402 -2.9665
alpha
LFrance/Germany -0.097026 0.057534 -0.0029306
LFrance -0.0030697 -0.0046797 -0.0066679
LGermany 0.0070976 0.029879 -0.0031577
long-run matrix, rank 3
LFrance/Germany LFrance LGermany
Constant
LFrance/Germany -0.11649 0.054180 0.011527 -
0.13170
LFrance -0.0018510 -0.0027252 0.0068069 -
0.014173
LGermany -0.0030948 0.031181 -0.072480
0.17440
SYS( 4) Cointegrated VAR
The dataset is: new09.in7
The estimation sample is: 1974(4) - 1990(2)
Cointegrated VAR (12) in:
[0] = LFrance/Germany
[1] = LFrance
[2] = LGermany
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta
LFrance/Germany 1.0000
LFrance 0.044039
LGermany -1.3365
Constant 4.1392
alpha

43. LFrance/Germany -0.097026
LFrance -0.0030697
LGermany 0.0070976
Standard errors of alpha
LFrance/Germany 0.019970
LFrance 0.0042744
LGermany 0.0047086
Restricted long-run matrix, rank 1
LFrance/Germany LFrance LGermany
Constant
LFrance/Germany -0.097026 -0.0042729 0.12968 -
0.40161
LFrance -0.0030697 -0.00013519 0.0041029 -
0.012706
LGermany 0.0070976 0.00031257 -0.0094863
0.029379
Standard errors of long-run matrix
LFrance/Germany 0.019970 0.00087944 0.026691
0.082659
LFrance 0.0042744 0.00018824 0.0057129
0.017692
LGermany 0.0047086 0.00020736 0.0062932
0.019490
Reduced form beta
LFrance/Germany -1.0000
LFrance -0.044039
LGermany 1.3365
Constant -4.1392
Standard errors of reduced form beta
LFrance/Germany 0.00000
LFrance 0.37250

44. LGermany 0.90508
Constant 2.2089
Moving-average impact matrix
-0.18798 16.848 4.7169
-0.62231 34.388 6.3657
-0.16115 13.738 3.7389
log-likelihood 2467.45781 -T/2log|Omega| 3280.50959
no. of observations 191 no. of parameters 105
rank of long-run matrix 1 no. long-run restrictions 0
beta is not identified
No restrictions imposed
LFrance/Germany: Portmanteau(12): 6.85112
LFrance : Portmanteau(12): 8.11577
LGermany : Portmanteau(12): 4.3378
LFrance/Germany: Normality test: Chi^2(2) = 33.424
[0.0000]**
LFrance : Normality test: Chi^2(2) = 38.314 [0.0000]**
LGermany : Normality test: Chi^2(2) = 3.1750 [0.2044]
LFrance/Germany: ARCH 1-7 test: F(7,142) = 1.1036
[0.3641]
LFrance : ARCH 1-7 test: F(7,142) = 0.12194 [0.9967]
LGermany : ARCH 1-7 test: F(7,142) = 0.44855 [0.8698]
LFrance/Germany: Hetero test: F(72,81) = 0.72380
[0.9184]
LFrance : Hetero test: F(72,81) = 0.70373 [0.9352]
LGermany : Hetero test: F(72,81) = 0.47543 [0.9992]
Vector Portmanteau(12): 58.9484
Vector Normality test: Chi^2(6) = 74.927 [0.0000]**
Vector Hetero test: F(432,463)= 0.60106 [1.0000]
SYS( 5) Estimating the system by OLS
The dataset is: new09.in7

45. The estimation sample is: 1974(4) - 1990(2)
URF equation for: LBelgium/Germany
Coefficient Std.Error t-value t-prob
LBelgium/Germany_1 1.24411 0.08057 15.4 0.0000
LBelgium/Germany_2 -0.429889 0.1303 -3.30 0.0012
LBelgium/Germany_3 0.242191 0.1348 1.80 0.0744
LBelgium/Germany_4 -0.0840452 0.1334 -0.630 0.5296
LBelgium/Germany_5 0.0963068 0.1260 0.764 0.4458
LBelgium/Germany_6 -0.184540 0.1258 -1.47 0.1446
LBelgium/Germany_7 0.102924 0.1285 0.801 0.4244
LBelgium/Germany_8 -0.0151956 0.1278 -0.119 0.9055
LBelgium/Germany_9 0.0137378 0.1228 0.112 0.9111
LBelgium/Germany_10 -0.0475944 0.1206 -0.395
0.6937
LBelgium/Germany_11 -0.0848517 0.1137 -0.746
0.4567
LBelgium/Germany_12 0.0888137 0.06890 1.29 0.1993
LBelgium_1 0.175739 0.1940 0.906 0.3664
LBelgium_2 -0.200036 0.2639 -0.758 0.4497
LBelgium_3 0.125802 0.2635 0.477 0.6337
LBelgium_4 -0.0591721 0.2655 -0.223 0.8239
LBelgium_5 0.160206 0.2678 0.598 0.5506
LBelgium_6 -0.228600 0.2653 -0.862 0.3902
LBelgium_7 -0.00589070 0.2654 -0.0222 0.9823
LBelgium_8 0.613126 0.2710 2.26 0.0250
LBelgium_9 -0.814964 0.2786 -2.93 0.0040
LBelgium_10 0.0607708 0.2843 0.214 0.8310
LBelgium_11 -0.0625811 0.2797 -0.224 0.8233
LBelgium_12 0.217344 0.1686 1.29 0.1992
LGermany_1 -0.373746 0.2162 -1.73 0.0859
LGermany_2 0.267891 0.3412 0.785 0.4336
LGermany_3 -0.00824147 0.3465 -0.0238 0.9811
LGermany_4 0.0151444 0.3493 0.0434 0.9655
LGermany_5 0.450110 0.3569 1.26 0.2092
LGermany_6 -0.376543 0.3550 -1.06 0.2905

46. LGermany_7 -0.351132 0.3493 -1.01 0.3164
LGermany_8 0.249408 0.3406 0.732 0.4651
LGermany_9 0.134627 0.3275 0.411 0.6816
LGermany_10 0.370252 0.3264 1.13 0.2584
LGermany_11 -0.204470 0.3263 -0.627 0.5319
LGermany_12 -0.0934401 0.2143 -0.436 0.6634
Constant -0.0804209 0.1089 -0.739 0.4613
sigma = 0.00614438 RSS = 0.00581402083
URF equation for: LBelgium
Coefficient Std.Error t-value t-prob
LBelgium/Germany_1 0.0564882 0.03530 1.60 0.1116
LBelgium/Germany_2 -0.0506352 0.05710 -0.887
0.3766
LBelgium/Germany_3 0.0121875 0.05907 0.206 0.8368
LBelgium/Germany_4 0.0364642 0.05844 0.624 0.5336
LBelgium/Germany_5 -0.0796239 0.05520 -1.44 0.1512
LBelgium/Germany_6 0.101231 0.05513 1.84 0.0683
LBelgium/Germany_7 -0.0832351 0.05629 -1.48 0.1413
LBelgium/Germany_8 0.0265802 0.05599 0.475 0.6356
LBelgium/Germany_9 -0.0570059 0.05381 -1.06 0.2911
LBelgium/Germany_10 0.0869395 0.05285 1.65 0.1020
LBelgium/Germany_11 -0.0532367 0.04982 -1.07
0.2870
LBelgium/Germany_12 0.0395195 0.03019 1.31 0.1924
LBelgium_1 0.951219 0.08498 11.2 0.0000
LBelgium_2 -0.140726 0.1156 -1.22 0.2255
LBelgium_3 -0.131885 0.1154 -1.14 0.2550
LBelgium_4 0.276431 0.1163 2.38 0.0187
LBelgium_5 -0.118454 0.1173 -1.01 0.3143
LBelgium_6 0.161914 0.1162 1.39 0.1656
LBelgium_7 -0.338599 0.1163 -2.91 0.0041
LBelgium_8 0.199237 0.1187 1.68 0.0953
LBelgium_9 0.0412499 0.1220 0.338 0.7358
LBelgium_10 -0.105923 0.1245 -0.850 0.3964

47. LBelgium_11 0.0981605 0.1225 0.801 0.4243
LBelgium_12 -0.00651130 0.07386 -0.0882 0.9299
LGermany_1 0.222759 0.09472 2.35 0.0199
LGermany_2 -0.293356 0.1495 -1.96 0.0515
LGermany_3 0.463101 0.1518 3.05 0.0027
LGermany_4 -0.370651 0.1531 -2.42 0.0166
LGermany_5 0.0287706 0.1564 0.184 0.8543
LGermany_6 1.07279e-005 0.1555 0.00 0.9999
LGermany_7 0.271382 0.1530 1.77 0.0781
LGermany_8 -0.00624830 0.1492 -0.0419 0.9667
LGermany_9 -0.128807 0.1435 -0.898 0.3707
LGermany_10 0.0195920 0.1430 0.137 0.8912
LGermany_11 -0.151840 0.1430 -1.06 0.2899
LGermany_12 0.0880479 0.09389 0.938 0.3498
Constant -0.229299 0.04770 -4.81 0.0000
sigma = 0.00269192 RSS = 0.001115951271
URF equation for: LGermany
Coefficient Std.Error t-value t-prob
LBelgium/Germany_1 -0.0362026 0.03033 -1.19 0.2344
LBelgium/Germany_2 0.0568306 0.04906 1.16 0.2485
LBelgium/Germany_3 0.0147421 0.05075 0.290 0.7718
LBelgium/Germany_4 -0.0108972 0.05021 -0.217
0.8285
LBelgium/Germany_5 -0.116697 0.04742 -2.46 0.0150
LBelgium/Germany_6 0.120452 0.04737 2.54 0.0120
LBelgium/Germany_7 -0.0318466 0.04837 -0.658
0.5112
LBelgium/Germany_8 -0.0253422 0.04810 -0.527
0.5991
LBelgium/Germany_9 0.0294442 0.04623 0.637 0.5252
LBelgium/Germany_10 -0.00683282 0.04541 -0.150
0.8806
LBelgium/Germany_11 -0.0270554 0.04281 -0.632
0.5283

48. LBelgium/Germany_12 0.0284262 0.02594 1.10 0.2748
LBelgium_1 0.0404842 0.07301 0.554 0.5801
LBelgium_2 -0.00894351 0.09935 -0.0900 0.9284
LBelgium_3 -0.168750 0.09917 -1.70 0.0909
LBelgium_4 0.288801 0.09992 2.89 0.0044
LBelgium_5 -0.238411 0.1008 -2.36 0.0193
LBelgium_6 0.133391 0.09987 1.34 0.1836
LBelgium_7 -0.105906 0.09988 -1.06 0.2907
LBelgium_8 -0.0980220 0.1020 -0.961 0.3380
LBelgium_9 0.289230 0.1049 2.76 0.0065
LBelgium_10 -0.164248 0.1070 -1.53 0.1268
LBelgium_11 -0.0314415 0.1053 -0.299 0.7656
LBelgium_12 0.0501439 0.06346 0.790 0.4306
LGermany_1 1.29590 0.08138 15.9 0.0000
LGermany_2 -0.311902 0.1284 -2.43 0.0163
LGermany_3 0.225749 0.1304 1.73 0.0855
LGermany_4 -0.310123 0.1315 -2.36 0.0196
LGermany_5 0.123547 0.1344 0.920 0.3592
LGermany_6 -0.224938 0.1336 -1.68 0.0943
LGermany_7 0.295004 0.1315 2.24 0.0263
LGermany_8 -0.103835 0.1282 -0.810 0.4192
LGermany_9 0.0448156 0.1233 0.364 0.7167
LGermany_10 -0.0346024 0.1229 -0.282 0.7786
LGermany_11 0.298141 0.1228 2.43 0.0164
LGermany_12 -0.274759 0.08066 -3.41 0.0008
Constant -0.0233588 0.04099 -0.570 0.5696
sigma = 0.00231282 RSS = 0.0008237694326
log-likelihood 2525.68367 -T/2log|Omega| 3338.73545
|Omega| 6.55862423e-016 log|Y'Y/T| -8.14095441
R^2(LR) 1 R^2(LM) 0.992103
no. of observations 191 no. of parameters 111
F-test on regressors except unrestricted: F(111,456) = 31811.5
[0.0000] **

49. F-tests on retained regressors, F(3,152) =
LBelgium/Germany_1 84.4832
[0.000]**LBelgium/Germany_2 4.84693 [0.003]**
LBelgium/Germany_3 1.19021 [0.315]
LBelgium/Germany_4 0.302757 [0.823]
LBelgium/Germany_5 2.17739 [0.093]
LBelgium/Germany_6 2.83358 [0.040]*
LBelgium/Germany_7 0.829163 [0.480]
LBelgium/Germany_8 0.253797 [0.859]
LBelgium/Germany_9 0.740966 [0.529]
LBelgium/Germany_10 1.08987 [0.355]
LBelgium/Germany_11 0.703625 [0.551]
LBelgium/Germany_12 1.53880 [0.207]
LBelgium_1 47.3689 [0.000]** LBelgium_2 0.824504
[0.482]
LBelgium_3 1.08271 [0.358] LBelgium_4 3.50152
[0.017]*
LBelgium_5 1.88295 [0.135] LBelgium_6 1.02400
[0.384]
LBelgium_7 2.88040 [0.038]* LBelgium_8 3.81197
[0.011]*
LBelgium_9 5.08111 [0.002]** LBelgium_10 0.814791
[0.488]
LBelgium_11 0.339140 [0.797] LBelgium_12 0.857423
[0.465]
LGermany_1 87.0156 [0.000]** LGermany_2 2.45571
[0.065]
LGermany_3 3.33343 [0.021]* LGermany_4 2.87626
[0.038]*
LGermany_5 0.906398 [0.440] LGermany_6 1.52991
[0.209]
LGermany_7 2.15385 [0.096] LGermany_8 0.388259
[0.762]
LGermany_9 0.465400 [0.707] LGermany_10
0.483026 [0.695]
LGermany_11 3.39496 [0.020]* LGermany_12

50. 5.56514 [0.001]**
Constant 8.75168 [0.000]**
correlation of URF residuals (standard deviations on diagonal)
LBelgium/Germany LBelgium LGermany
LBelgium/Germany 0.0061444 -0.16532 -0.11966
LBelgium -0.16532 0.0026919 0.34182
LGermany -0.11966 0.34182 0.0023128
correlation between actual and fitted
LBelgium/Germany LBelgium LGermany
0.99917 0.99996 0.99991
I(1) cointegration analysis, 1974(4) - 1990(2)
eigenvalue loglik for rank
2492.611 0
0.21606 2515.858 1
0.081106 2523.936 2
0.018136 2525.684 3
H0:rank<= Trace test [ Prob]
0 66.145 [0.000] **
1 19.651 [0.059]
2 3.4957 [0.504]
Asymptotic p-values based on: Restricted constant
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta (scaled on diagonal; cointegrating vectors in columns)
LBelgium/Germany 1.0000 0.39584 0.030822
LBelgium -2.6147 1.0000 -0.57142
LGermany 3.1370 -1.8566 1.0000
Constant -5.2325 2.3655 -1.9104
alpha

51. LBelgium/Germany -0.027470 -0.078750 0.019827
LBelgium 0.040111 -0.010946 -0.0033899
LGermany 0.0018460 -0.016235 -0.012932
long-run matrix, rank 3
LBelgium/Germany LBelgium LGermany
Constant
LBelgium/Germany -0.058031 -0.018254 0.079858 -
0.080421
LBelgium 0.035674 -0.11389 0.14276 -0.22930
LGermany -0.0049789 -0.013672 0.023001 -
0.023359
SYS( 6) Cointegrated VAR
The dataset is: new09.in7
The estimation sample is: 1974(4) - 1990(2)
Cointegrated VAR (12) in:
[0] = LBelgium/Germany
[1] = LBelgium
[2] = LGermany
Restricted variables:
[0] = Constant
Number of lags used in the analysis: 12
beta
LBelgium/Germany 1.0000
LBelgium -2.6147
LGermany 3.1370
Constant -5.2325
alpha
LBelgium/Germany -0.027470
LBelgium 0.040111
LGermany 0.0018460

52. Standard errors of alpha
LBelgium/Germany 0.015225
LBelgium 0.0064922
LGermany 0.0056482
Restricted long-run matrix, rank 1
LBelgium/Germany LBelgium LGermany
Constant
LBelgium/Germany -0.027470 0.071826 -0.086175
0.14374
LBelgium 0.040111 -0.10488 0.12583 -0.20988
LGermany 0.0018460 -0.0048267 0.0057910 -
0.0096593
Standard errors of long-run matrix
LBelgium/Germany 0.015225 0.039808 0.047761
0.079665
LBelgium 0.0064922 0.016975 0.020366
0.033970
LGermany 0.0056482 0.014768 0.017719
0.029554
Reduced form beta
LBelgium/Germany -1.0000
LBelgium 2.6147
LGermany -3.1370
Constant 5.2325
Standard errors of reduced form beta
LBelgium/Germany 0.00000
LBelgium 0.47463
LGermany 0.72964
Constant 1.0775
Moving-average impact matrix
1.3452 0.54091 8.2649

53. 0.61395 -0.35713 16.896
0.082895 -0.47009 11.448
log-likelihood 2515.85803 -T/2log|Omega| 3328.90981
no. of observations 191 no. of parameters 105
rank of long-run matrix 1 no. long-run restrictions 0
beta is not identified
No restrictions imposed
LBelgium/Germany: Portmanteau(12): 5.96898
LBelgium : Portmanteau(12): 3.39841
LGermany : Portmanteau(12): 6.49229
LBelgium/Germany: Normality test: Chi^2(2) = 121.37
[0.0000]**
LBelgium : Normality test: Chi^2(2) = 6.3458 [0.0419]*
LGermany : Normality test: Chi^2(2) = 2.1111 [0.3480]
LBelgium/Germany: ARCH 1-7 test: F(7,142) = 0.42037
[0.8884]
LBelgium : ARCH 1-7 test: F(7,142) = 0.66839 [0.6985]
LGermany : ARCH 1-7 test: F(7,142) = 0.12698 [0.9963]
LBelgium/Germany: Hetero test: F(72,81) = 0.66325
[0.9616]
LBelgium : Hetero test: F(72,81) = 0.37190 [1.0000]
LGermany : Hetero test: F(72,81) = 0.49807 [0.9986]
Vector Portmanteau(12): 52.0286
Vector Normality test: Chi^2(6) = 120.49 [0.0000]**
Vector Hetero test: F(432,463)= 0.69746 [0.9999]

54. （4）AR
图acf 和Pasf
---- Maximum likelihood estimation of ARFIMA(4,0,0) model --
--
The estimation sample is: 1973(5) - 1990(2)
The dependent variable is: DLFrance/Belgium
The dataset is: new09.in7
Coefficient Std.Error t-value t-prob
AR-1 0.382891 0.06996 5.47 0.000
AR-2 -0.0181099 0.07466 -0.243 0.809
AR-3 -0.0856939 0.07447 -1.15 0.251
AR-4 -0.0745809 0.06953 -1.07 0.285
Constant 0.00177940 0.0009659 1.84 0.067
log-likelihood 625.927726
no. of observations 202 no. of parameters 6
AIC.T -1239.85545 AIC -6.13789827
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
sigma 0.0109093 sigma^2 0.000119013
BFGS using numerical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence

55. Used starting values:
0.38482 -0.018468 -0.086797 -0.075880 0.0017844
---- Maximum likelihood estimation of ARFIMA(3,0,0) model --
--
The estimation sample is: 1973(5) - 1990(2)
The dependent variable is: DLFrance/Belgium
The dataset is: new09.in7
Coefficient Std.Error t-value t-prob
AR-1 0.391643 0.06968 5.62 0.000
AR-2 -0.0169831 0.07482 -0.227 0.821
AR-3 -0.114939 0.06940 -1.66 0.099
Constant 0.00178156 0.001040 1.71 0.088
log-likelihood 625.354221
no. of observations 202 no. of parameters 5
AIC.T -1240.70844 AIC -6.142121
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
sigma 0.0109409 sigma^2 0.000119704
BFGS using numerical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence
Used starting values:
0.39367 -0.017166 -0.11667 0.0017844
---- Maximum likelihood estimation of ARFIMA(2,0,0) model --
--
The estimation sample is: 1973(5) - 1990(2)
The dependent variable is: DLFrance/Belgium
The dataset is: new09.in7
Coefficient Std.Error t-value t-prob

56. AR-1 0.399155 0.07004 5.70 0.000
AR-2 -0.0633158 0.06988 -0.906 0.366
Constant 0.00178289 0.001164 1.53 0.127
log-likelihood 623.986982
no. of observations 202 no. of parameters 4
AIC.T -1239.97396 AIC -6.13848497
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
sigma 0.0110163 sigma^2 0.000121359
BFGS using numerical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence
Used starting values:
0.40113 -0.063965 0.0017844
---- Maximum likelihood estimation of ARFIMA(1,0,0) model --
--
The estimation sample is: 1973(5) - 1990(2)
The dependent variable is: DLFrance/Belgium
The dataset is: new09.in7
Coefficient Std.Error t-value t-prob
AR-1 0.375174 0.06496 5.78 0.000
Constant 0.00178020 0.001239 1.44 0.152
log-likelihood 623.577387
no. of observations 202 no. of parameters 3
AIC.T -1241.15477 AIC -6.14433056
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
sigma 0.0110389 sigma^2 0.000121857
BFGS using numerical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence

57. Used starting values:
0.37701 0.0017844
Test for excluding: AR-1
Subset Chi^2(1) = 33.3597 [0.0000] **
Descriptive statistics for residuals:
Normality test: Chi^2(2) = 58.149 [0.0000]**
ARCH 1-1 test: F(1,198) = 7.5716 [0.0065]**
Portmanteau(36): Chi^2(35) = 47.627 [0.0755]
ARCH
ARCH coefficients:
Lag Coefficient Std.Error
1 0.14213 0.07377
2 0.15012 0.0743
3 0.16443 0.07515
4 -0.028656 0.07482
5 0.047427 0.07478
6 -0.039926 0.07482
7 -0.013674 0.07469
8 -0.011489 0.07465
9 0.029838 0.07458
10 -0.0027954 0.07309
11 -0.052836 0.07233
12 0.020861 0.07185
RSS = 1.47674e-005 sigma = 0.000289665
Testing for error ARCH from lags 1 to 12
ARCH 1-12 test: F(12,176) = 1.7613 [0.0579]
Residual [1973( 5) - 1990( 2)] saved to new09.in7

58. GARCH
VOL( 2) Modelling DLFrance/Belgium by restricted
GARCH(1,1)
The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error robust-SE t-value t-prob
Constant X 0.00137385 0.0005496 0.0006335 2.17
0.031
alpha_0 H 2.53091e-005 6.838e-006 1.225e-005 2.07
0.040
alpha_1 H 0.548753 0.1647 0.2417 2.27 0.024
beta_1 H 0.386169 0.1059 0.1239 3.12 0.002
log-likelihood 647.090499 HMSE 7.74626
mean(h_t) 0.000169302 var(h_t) 5.89695e-008
no. of observations 202 no. of parameters 4
AIC.T -1286.181 AIC -6.36723266
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
alpha(1)+beta(1) 0.934922 alpha_i+beta_i>=0,
alpha(1)+beta(1)<1
Initial terms of alpha(L)/[1-beta(L)]:
0.54875 0.21191 0.081834 0.031602 0.012204
0.0047127
0.0018199 0.00070278 0.00027139 0.00010480 4.0472e-
005 1.5629e-005
Used sample mean of squared residuals to start recursion
Robust-SE based on analytical Information matrix and
analytical OPG matrix
BFGS using analytical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence
Used starting values:
0.0017844 2.1595e-005 0.70855 0.13943

59. Test for excluding: alpha_1
Subset Chi^2(1) = 11.0952 [0.0009] **
Using robust standard errors:
Subset Chi^2(1) = 5.15536 [0.0232] *
Portmanteau statistic for scaled residuals
Autocorrelation function (ACF) from lag 1 to 12:
0.24488 0.047178 -0.058108 -0.085325 -0.059613
-0.080555
-0.0051672 0.13997 0.19257 0.0078786 -0.13371
-0.15760
Partial autocorrelation function (PACF):
0.24488 -0.013605 -0.070740 -0.057554 -0.023454
-0.065465
0.024169 0.14067 0.12540 -0.091215 -0.13049
-0.078908
Portmanteau(12): Chi^2(12) = 38.040 [0.0002]**
Portmanteau statistic for squared scaled residuals
Autocorrelation function (ACF) from lag 1 to 12:
-0.011257 0.027938 -0.024482 0.032919 0.050857
-0.051928
-0.035495 -0.054797 0.075378 0.023350 -0.028213
0.0044665
Partial autocorrelation function (PACF):
-0.011257 0.027815 -0.023885 0.031675 0.052970
-0.053474
-0.038122 -0.051434 0.071194 0.027495 -0.027254
0.010154
Portmanteau(12): Chi^2(10) = 4.0149 [0.9467]
EGARCH
VOL( 3) Modelling DLFrance/Belgium by EGARCH(1,1)

60. The dataset is: new09.in7
The estimation sample is: 1973(5) - 1990(2)
Coefficient Std.Error robust-SE t-value t-prob
Constant X 0.00101843 0.0005399 0.0005579 1.83
0.069
alpha_0 H -1.41749 0.6391 0.9994 -1.42 0.158
eps[-1] H -0.143496 0.09108 0.1445 -0.993 0.322
|eps[-1]| H 0.691818 0.1431 0.2420 2.86 0.005
beta_1 H 0.833174 0.07042 0.1136 7.33 0.000
log-likelihood 649.124517 HMSE 8.68633
mean(h_t) 0.000159174 var(h_t) 4.75962e-008
no. of observations 202 no. of parameters 5
AIC.T -1288.24903 AIC -6.37747046
mean(DLFrance/Belgium) 0.00178439
var(DLFrance/Belgium) 0.000142048
Used sample mean of squared residuals to start recursion
Robust-SE based on numerical Hessian matrix and numerical
OPG matrix
BFGS using numerical derivatives (eps1=0.0001; eps2=0.005):
Strong convergence
Used starting values:
0.0017844 1.0047 0.70855 0.00000 0.13943
(5) Forecast
Forecasting DLFrance/Belgium from 1990(3) to 1991(5)
Horizon Forecast (SE) Actual CondVar
1.0000 0.0010184 0.0051081 0.00013464 2.6093e-

61. 005
2.0000 0.0010184 0.0060643 -0.00097591 3.6775e-
005
3.0000 0.0010184 0.0069962 0.0043737 4.8947e-
005
4.0000 0.0010184 0.0078812 0.0029580 6.2113e-
005
5.0000 0.0010184 0.0087034 -0.0045257 7.5749e-
005
6.0000 0.0010184 0.0094536 0.0019288 8.9370e-
005
7.0000 0.0010184 0.010128 -0.0019952 0.00010257
8.0000 0.0010184 0.010726 -0.0011920 0.00011505
9.0000 0.0010184 0.011251 0.0031894 0.00012660
10.000 0.0010184 0.011709 0.0056647 0.00013710
11.000 0.0010184 0.012104 .NaN 0.00014651
12.000 0.0010184 0.012443 .NaN 0.00015484
13.000 0.0010184 0.012734 .NaN 0.00016214
14.000 0.0010184 0.012980 .NaN 0.00016849
mean(Error) = -6.2387e-005 RMSE = 0.0030268
SD(Error) = 0.0030261 MAPE = 165.93
FMBF computer lab1.pdf
FMBF: Computer Practical 1
Introduction
There are four workshops for the FMBF module this term which
will be organised as
follows:
Practical 1 ARIMA modelling and unit root testing.
Practical 2 Cointegration procedures.

62. Practical 3 ARCH/GARCH modelling and forecasting.
1 ARIMA Modelling
1.1 Aims
In the first part of this session we will firstly load a dataset and
experiment with ARIMA
modelling. Once the concept has been demonstrated you will be
required to find a preferred
model for the stock price data that we will be using. The stock
price series is raw data so you
will need to calculate returns yourself using the calculator
function in PcGive.
We will demonstrate the procedure for using the Time Series
Models package in PcGive by
estimating an AR(1) model:
1.2 Key Steps
Importing and transforming the data
1. We will be using monthly data on the price of British
Airways from 1996 to 2002.
Download the file BA.xls from duo that contains these data.
2. Start PcGive.
(Start > Search PcGive12)

63. 3. Create new database in PcGive.
(File > New… > OxMetrics (Data: *.in7) > Frequency: Monthly
> Observations: 74 > OK).
Practical 4 Review.
4. Copy the price data column from Excel to PcGive. Double
click on the first row and type
the column title: BA.
Note: You could also click File > Open data file... and import
the Excel file directly.
However, PcGive will not automatically recognise the dates in
the leftmost column. If you
chose to do it this way you could choose Edit > Change Sample
to let PcGive know we are
dealing with monthly data from 1996.
5. Use Calculator to calculate the log return, i.e., generate new
series Ri which equals the
dlog of BA.

64. Prior to constructing the model
You should plot and carefully examine the ACF and PACF.
Recall that we plotted the ACF
and PACF last term, and that you can do this by going to the
Graphics button in PcGive.
(Graphics > Choose the variables and click All plot types >
Time-series properties > In
Dynamic Properties tick ACF and PACF and click OK)
Is a particular model suggested by this graphical analysis?
Constructing the model
These steps show the construction of an AR(1) model for
demonstration.
1 In PcGive select Model > Category: Models for time series
data > Model class: ARFIMA
models using PcGive.
2 Select Formulate…
3 Select Ri as the dependent variable (Y), add a constant term
(PcGive should do this
automatically), and press OK.

65. 4 Set AR order as 1 and fix the Fractional parameter d at 0.
Treatment of the mean should
automatically be set to None (or using constant as regressor).
5 Press OK, and select Maximum Likelihood.
6 Press OK and the Estimation Results will appear.
7 Examine the results. Is this model satisfactory?
Exercice 1: Identifying your preferred model
Carefully examine the results from your model. You should:
using ACF and PACF and the Q-
statistic (Ljung Box statistic).
-estimate the model, overfitting in an effort to isolate the
preferred specification.
competing models.
If you are not prompted to do so by the steps above, you should

66. at the least estimate an MA(1)
and an ARIMA(1,0,1) model to be clear on the procedure of
specifying such models in
PcGive.
2 Unit root testing
2.1 Aims
In the second part of this session we will examine stationarity
testing using PcGive.
Price/Earnings data for the US will be used to demonstrate how
the software can easily test
for the presence of a unit root and display results in a fashion
that easily allows us to choose a
preferred model cf. the number of lags to include. We will then
test for stationarity in
monthly data for the FTSE 100 and FTSE All Share.
Example 1: Annual Price/Earnings Ratio
This example is based on the illustration of the annual
price/earnings ratio proposed in
Verbeek (2004, p.274). The literature has focussed on whether
the price/earnings ratio is
mean reverting (why might this be interesting?).

67. 1 Load the data PE.xls into PcGive (File > Open… > PE.xls).
This is annual data on the
ratio of the S&P Composite Stock Price Index and S&P
Composite Earnings. The sample
(annual data) runs from 1871 to 2002.
2 Plot the log of the series (LOGPE) using GiveWin graphics
(Graphics > Choose LOGPE >
Actual series) . Does it look stationary?
3 We will test for stationarity with the standard Dickey-Fuller
regression, i.e. if we denote
the log P/E ratio as Yt
1 1t t t
(1)
Note that you will need to use Calculator to diff the LOGPE
series.
Modelling this using Single equation dynamic modelling...
gives
1
0.335 0.125

68. t t t
Y Y e
(2)
(Model > Category: Model for time-series data > Model class:
Single-equation Dynamic
Modelling using PcGive > Formulate… > Select DLOGPE as Y
and choose lagged
LOGPE > Click OK)
The full output from PcGive is
We can calculate the DF test statistic as -2.57, the 5% critical
value being -2.88. Thus we
cannot reject the null of a unit root. However, for this result to
hold we must have included
lags to the extent that the error term is white noise.
2.2 Automated unit root testing
Fortunately, PcGive makes it easy to perform unit root testing
automatically, saving us
having to run a regression each time. It also produces a neat
summary table allowing easy

69. selection of the appropriate number of lag terms.
We will first replicate the results previously obtained:
1 Select Model > Category: Other models > Model class:
Descriptive Statistics using
PcGive)
2 Select Formulate
3 Add LOGPE to the model and click OK
4 In Descriptive Statistics select Unit-root tests, and then edit
Unit-root test settings so that
Lag length for differences is 0 and Constant) is selected
5 Click OK and then OK in the Estimate Model dialog
6 The following results should appear in the Results area in
GiveWin
These are the results we obtained previously. Note that the
software automatically calculates
the correct test statistic and critical value.
2.3 ADF testing
We will now add lags and look at the results from augmented
Dickey-Fuller tests:

70. 1 Formulate a new model (Descriptive Statistics)
2 Edit Unit-root test settings so that Lag length for differences
is 6 and Constant) is selected.
Make sure that Report summary table only is selected.
The following results are presented
There is a rejection of the null of a unit root at the 5% level
with one lag. However, none of
the other ADF tests reject the null of nonstationarity. Does this
concur with the graphical plot
of the P/E series that you produced above?
Exercice 2: Annual Price/Earnings Ratio cont...
Test for the presence of a second unit root in annual
price/earnings data (Hint: you will need
to difference the data once more). Can you reject the null of
nonstationarity? What
conclusion does this lead you towards?
Exercice 3: Stationarity in the FTSE 100 and ALL SHARE
1. Load the data FTSEDATA.xls that is on duo. This contains
monthly data for the FTSE 100
and ALL SHARE from 1985:1.
2. Create logarithms of the two indices, naming them LFTSE100

71. and LFTALLSH.
3. Plot the series then test for stationarity adding an appropriate
number of lags.
4. Create the first difference of LFTSE100 and LFTALLSH and
test for stationarity after
plotting the differenced series.
5. Come to conclusions about the presence of a unit root in the
two series.
2.4 Points to note
unit root test output mean;
see Figure 1 and Figure 2.
unit root in ammore systematic
way (see Harris and Sollis p. 47 and your lecture notes). This
will not be considered here.
References
M. Verbeek. A Guide to Modern Econometrics. John Wiley &
Sons, Inc., 2004.
Figure 1: Interpreting unit root test output: summary table
option

72. Figure 2: Interpreting unit root test output: summary table vs.
standard output
Guide_to_ACF_PACF_plots(computer lab1).pdf
Guide to ACF/PACF Plots
The plots shown here are those of pure or theoretical ARIMA
processes. Here are
some general guidelines for identifying the process:
Nonstationary series have an ACF that remains significant for
half a dozen or
more lags, rather than quickly declining to zero. You must
difference such a
series until it is stationary before you can identify the process.
Autoregressive processes have an exponentially declining ACF
and spikes
in the first one or more lags of the PACF. The number of spikes
indicates the
order of the autoregression.
Moving average processes have spikes in the first one or more
lags of the ACF
and an exponentially declining PACF. The number of spikes
indicates the order of
the moving average.

73. Mixed (ARMA) processes typically show exponential declines
in both the
ACF and the PACF.
At the identification stage, you do not need to worry about the
sign of the ACF or
PACF, or about the speed with which an exponentially declining
ACF or PACF
approaches zero. These depend upon the sign and actual value
of the AR and MA
coefficients. In some instances, an exponentially declining ACF
alternates between
positive and negative values.
ACF and PACF plots from real data are never as clean as the
plots shown here.
You must learn to pick out what is essential in any given plot.
Always check the ACF
and PACF of the residuals, in case your identification is wrong.
Bear in mind that:
Seasonal processes show these patterns at the seasonal lags (the
multiples of
the seasonal period).
1
2
You are entitled to treat nonsignificant values as zero. That is,
you can ignore
values that lie within the confidence intervals on the plots. You
do not have to
ignore them, however, particularly if they continue the pattern

74. of the statistically
significant values.
An occasional autocorrelation will be statistically significant by
chance alone.
You can ignore a statistically significant autocorrelation if it is
isolated, preferably
at a high lag, and if it does not occur at a seasonal lag.
Consult any text on ARIMA analysis for a more complete
discussion of ACF and
PACF plots.
ARIMA(0,0,1), θ>0
ACF PACF
3
Guide to ACF/PACF Plots
ARIMA(0,0,1), θ<0
ACF PACF
ARIMA(0,0,2), θ1θ2>0
ACF PACF
4
ARIMA(1,0,0), φ>0

75. ACF PACF
ARIMA(1,0,0), φ<0
ACF PACF
5
Guide to ACF/PACF Plots
ARIMA(1,0,1), φ<0, θ>0
ACF PACF
ARIMA(2,0,0), φ1φ2>0
ACF PACF
6
ARIMA(0,1,0) (integrated series)
ACF
Table of Contents1. Guide to ACF/PACF PlotsIndex
FMBF computer lab2.pdf
FMBF: Computer Practical 2

76. Introduction
This workshop session covers cointegration, using the Engle-
Granger and Johansen
approaches. You should be aware of the benefits and drawbacks
of each approach.
1 Engle-Granger
Exercise 1: Cointegration between the S&P and FTSE All-Share
1. Load the data file FMBF Prac2.xls from duo. This contains
monthly data on the
S&P 500 and FTSE All Share from January 1 1965 to January 1
2004.
2. Log both series (Calculator) and then use the unit root testing
facility in
Descriptive Statistics to assess the degree of integration of the
series (Model >
Category: Other models; Model class: Descriptive statistics
using PcGive).
Notes: most financial variables are I(1) series. To conduct the
EG procedure, we
should firstly check whether the two time series are I(1).
3. Regress LS&P on LFTSE and a constant using OLS (Model >
Category:
Models for time-series data; Model class: Single-equation
dynamic

77. Modelling using PcGive).
4. Save the cointegration regression residual in the database
(Test > Test Menu:
Store Residuals etc. in Database… > Store in database:
Residuals).
5. Test for cointegration by performing a unit-root test on the
saved residuals (do
not include deterministic components here).
6. Evaluate the results and establish whether or not the series
cointegrate (note:
make sure you use the correct critical values).
7. If appropriate, build an ECM. Do this by regressing DLS&P
on a constant,
DLFTSE and the one-period lagged residuals that were
previously stored in the
database. Interpret your findings.
Notes: according to the unit root test of the residuals, since the

78. residuals are not
stationary, it is not appropriate to put the non-stationary
residuals into the ECM.
In other words, the residuals are I(1). Therefore, we should
estimate a model
containing only first differences.
2 Johansen
Example 1: Long-run PPP
This is a PcGive implementation of the long-run purchasing
power parity example
presented in Verbeek (2004, p.331). We begin by loading the
data file ppp.xls from
duo, which contains monthly observations from 1981:1 to
1996:6 on price indices and
exchange rates from France and Italy. The variables contained
in the file are as
follows:
This example investigates the concept of PPP, where exchange
rate equals the ratio of
price levels. In logarithms, we represent PPP as:
*

79. ttt
(1)
where t
s
is the log of the spot exchange rate, t
p
is the log of domestic prices and
*
t
p
is the log of foreign prices.
1. Following Verbeek's reasoning we will first run a test with p
= 3, excluding a
time trend (Model > Category: Models for time-series data;
Model class:
Multiple-equation dynamic Modelling using PcGive). Note that
PcGive
automatically restricts the Constant term (shown by the U to its
left. We remove
this to restrict the constant following Verbeek's example. Select
U Constant in

80. Selection > Change Use default status to Clear status and click
Set, then the
U is removed. Note that this now corresponds to Model 2 in the
Pantula
Principle). Click OK and choose Unrestricted system.
2. Press Test > Test Menu: Dynamic Analysis and Cointegration
Tests... >
Dynamic Analysis: I(1) cointegration analysis > OK. You are
presented with
results, the firrst part of which are the eigenvalues:
We can see from the results that there are two small eigenvalues
that are significant at
the 1 percent level. In this case we reject H0 : r = 0 and also H0
: r = 1, but we cannot
reject H0 : r = 2 against the alternative of H1 : r = 3. Therefore
using Johansen we
conclude that there are two cointegrating relationships. P-values
are based on Doornik
(1998) (reprinted in McAleer and Oxley (1999)). Verbeek
(2004, p.332) reminds us
that in this particular example, Engle-Granger finds that the null

81. of no cointegration
could not be rejected. (Note: you can follow the E-G procedure
that was used above to
verify this). One possible explanation is that the number of lags
is too small.
Therefore we formulate a model with p = 12, supported by the
use of monthly data:
These results are clearly weaker than with p = 3. We do,
however, have a rejection of
H0 : r = 1. We can now move on to build a cointegrated VAR
model. We will assume
r = 1.
3. Formulate the model used for estimating the cointegration
test for p = 12.
Remember that we have a restricted constant (Model >
Category: Models for
time-series data; Model class: Multiple-equation dynamic
Modelling using
PcGive).
4. Click OK and then select Cointegrated VAR and press OK
once more.

82. 5. In the Cointegrated VAR Settings dialog box make sure the
Cointegrating rank is
set to 1. Click OK and OK to estimate a Reduced Rank
Regression
You should be presented with the following output in the
Results:
The most interesting part of these results, relating to estimating
the cointegrating
vector, β, are shown under Reduced form beta. The normalized
cointegrating
therefore corresponds to:
*
756.14346.6
ttt
As Verbeek, p.332 points out, this “does not seem to correspond
to an economically
interpretable long-run relationship.”

83. 3 The Pantula Principle
Following Johansen (1992) we can use the so-called Pantula
Principle to determine
the choice for deterministic components in the cointegration
space and/or the
short-run, and also establish the order of the cointegration rank
r. Recall that we
estimate all three models and present the results from the r = 0
(model 2, the most
restrictive) to r = n-1 (model 4, the least restrictive). Moving
through these models
and examining them in turn, we look to the trace statistic and
stop once the null
hypothesis cannot be rejected. In the case of the example we are
concerned with
identifying the deterministic components. One further point to
consider are the correct
critical values for models 1 to 4.
Exercice 2: The Pantula Principle
In the above worked example we estimated a long-run PPP
model and tested for

84. cointegration. Effectively, what we did corresponds with Model
2 in the Pantula
Principle.
timating Models 2, 3
and 4 in sequence.
You should examine your results and establish which
specification is preferred.
To assist you, Table 1 contains pointers on setting up each
model in PcGive. It is
helpful to construct a table similar to Table 5.5 in Harris and
Sollis (2003).
You should come to
your own conclusion about this by first looking at appropriate
graphic analysis.
Specifically you can go to Test > Graphic Analysis and look at
Actual and
fitted values, Cross plot of actual and fitted, Residuals (scaled),
Residual
density and histogram (kernel estimate) and Residual
correlogram (ACF).
preferred model. You should

85. examine F-tests on the retained regression to see if it is possible
to delete all the
lags of the same length (i.e. those that are not significant)
whilst keeping the
sample period unchanged. You can use Test > Exclusion
Restrictions... to
evaluate.
Summary for
equation-by-equation and system-wide tests, which you should
examine.
3.1 Imposing Restrictions
We can test for restrictions on α and β with PcGive. For
example, to test the
restriction
We would go to Model > Category: Models for time-series data;
Model class:
Multiple-equation dynamic Modelling using PcGive and select
Cointegrated VAR.

86. Press OK and enter a Cointegrating rank of 1. We then select
General restrictions
and press OK.
The General Restrictions dialog box opens, where we specify
the restriction in the
form &1=0;&2=0;&3=0 - see Figure 2 for a screenshot. We are
testing a null of
weakly exogenous - you may wish to try this for the PPP model
estimated above.
We can also use PcGive's ability to impose general restrictions
to test for unique
cointegrating vectors and in addition jointly test restrictions on
α and β. See Harris
and Sollis (2003, p.135-163) for full details, examples and
references to imposing
restrictions in PcGive.
4 Points to note

87. -
G and Johansen
approaches to cointegration.
whether the smallest k
- r0 eigenvalues significantly differ from 0. However, we can
also use the
maximum eigenvalue test. This tests H0 : r ≤ r0 against H1 : r =
r0 + 1. PcGive
gives the eigenvalues so it is possible to calculate these. For
example, in the PPP
example the first eigenvalue is 0.30091 so the ax
m
as 183*LN(1-0.30091), i.e. 65.509 which can be set against the
correct critical
value, in this case 22.04.
References
J. A. Doornik. Approximations to the asymptotic distribution of
cointegration tests.

88. Journal of Economic Surveys, 12:573{593, 1998.
R. Harris and R. Sollis. Apple Time Series Modelling and
Forecasting. John Wiley &
Sons Ltd., Chichester, 2003.
D. F. Hendry and J. A. Doornik. Empirical Econometric
Modelling Using Pc-Give,
volume 1. Timberlake Consultants Ltd., 3 edition, 2001.
S. Johansen. Cointegration in partial systems and the effciency
of single equation
analysis. Journal of Econometrics, 52:389{402, 1992.
M. McAleer and L. Oxley. Practical Issues in Cointegration
Analysis. Blackwell
Publishers, Oxford, 1999.
M. Verbeek. A Guide to Modern Econometrics. John Wiley &
Sons, Inc., 2004.
Johansen Test by PcGive(computer lab2).pdf
— Appendix ————-—
Cointegration Analysis Using the
Johansen Technique: A Practitioner's
__ Guide to PcGive 10.1

89. This appendix provides a basic introduction on how to
implement the Johan-
sen technique using the PcGive 10.1 econometric program (see
Doornik and
Hendry, 2001 for full details). Using the same data set as
underlies much of the
analysis in Chapters 5 and 6, we show the user how to work
through Chapter 5
up to the point of undertaking joint tests involving restrictions
on a and p.
This latest version of PcGive brings together the old PcGive
(single equa-
tion) and PcFiml (multivariate) stand-alone routines into a
single integrated
software program (that in fact is much more than the sum of the
previous
versions, since it is built on the Ox programming language and
allows
various bolt-on Ox programs to be added—such as dynamic
panel data
analysis (DPD), time series models and generalized
autoregressive conditional
heteroscedastic (GARCH) models—see Chapter 8). It is very
flexible to
operate, providing drop-down menus and (for the present
analysis) an
extensive range of modelling features for 7(1) and 7(0) systems
(and limited
analysis of the 7(2) system).1 Cointegration facilities are
embedded in an
overall modelling strategy leading through to structural vector
autoregression
(VAR) modelling.

90. After the data have been read-in to GiveWin2 (the data
management and
graphing platform that underpins PcGive and the other programs
that can
operate in what has been termed the Oxmetrics suite of
programs), it is first
necessary to (i) start the PcGive module, (ii) select 'Multiple-
equation Dynamic
Modelling' and then (iii) 'Formulate' a model. This allows the
user to define the
model in (log) levels, fix which deterministic variables should
enter the co-
integration space, determine the lag length of the VAR and
decide whether
1 PcGive also allows users to run batch jobs where previous
jobs can be edited and rerun.
2 The program accepts data files based on spreadsheets and
unformatted files.
260 APPENDIX
Figure A.I. Formulating a model in PcGive 10.1: Step (1)
choosing the correct model
option.
7(0) variables, particularly dummies, need to be specified to
enter the model in
the short-run dynamics but not in the cointegration spaces (see
Figures A. 1 and
A.2).
When the 'Formulate' option is chosen, the right-hand area
under 'Data-

91. base' shows the variables available for modelling. Introducing
dummies and
transformations of existing variables can be undertaken using
the 'Calculator'
or 'Algebra Editor' under Tools' in GiveWin, and these new
variables when
created will also appear in the 'Database'. In this instance, we
will model the
demand for real money (rm) as a function of real output (y),
inflation (dp) and
the interest rate (rstar), with all the variables already
transformed into log
levels. The lag length (k) is set equal to 4 (see lower right-hand
option in
Figure A.2); if we want to use an information criterion (1C) to
set the lag
length, then k can be set at different values, and when the model
is estimated
it will produce the Akaike, Hannan—Quinn and Schwarz 1C for
use in deter-
mining which model is appropriate.3 (However, it is also
necessary to ensure
that the model passes diagnostic tests with regard to the
properties of the
residuals of the equations in the model—see below—and
therefore use of an
1C needs to be done carefully.)
Each variable to be included is highlighted in the 'Database'
(either one at
a time, allowing the user to determine the order in which these
variables enter,
or all variables can be simultaneously highlighted). This will
bring up an
'<<Add' option, and, once this is clicked on, then the model
selected appears

92. on the left-hand side under 'Model'. The 'Y' next to each
variable indicates
3 Make sure you have this option turned on as it is not the
default. To do this in PcGive.
choose 'Model', then 'Options', 'Additional output' and put a
cross in the information
criterion box.
APPENDIX , 261
Figure A.2. Formulating a model in PcGive 10.1: Step (2)
choosing the 'Formulate'
option.
that it is endogenous and therefore will be modelled, a 'IT
indicates the vari-
able (e.g., the Constant, which enters automatically) is
unrestricted and will
only enter the short-run part of the vector error correction
model (VECM),
and the variables with '_k' next to them denote the lags of the
variable (e.g.,
rmt – 1).
We also need to enter some dummies into the short-run model to
take
account of'outliers' in the data (of course we identify these only
after estimating
the model, checking its adequacy, and then creating
deterministic dummies to
try to overcome problems; however, we shall assume we have
already done this,4

93. 4 In practice, if the model diagnostics—see Figure A.3—
indicates, say, a problem of
non-normality in the equation determining a variable, plot the
residuals using the
graphing procedures (select, in PcGive, 'Test' and 'Graphic
analysis' and then choose
'Residuals' by putting a cross in the relevant box). Visually
locate outliers in terms of
when they occur, then again under 'Test' choose 'Store residuals
in database', click on
residuals and accept the default names (or choose others) and
store these residuals in the
spreadsheet. Then go to the 'Window' drop-down option in Give
Win and select the
database, locate the residuals just stored, locate the outlier
residuals by scrolling down
the spreadsheet (using the information gleaned from the
graphical analysis) and then
decide how you will 'dummy out' the outlier (probably just by
creating a dummy
variable using the 'Calculator' option in Give Win, with the
dummy being 0 before and
after the outlier date and 1 for the actual date of the outlier).
262 APPENDIX
or that ex ante we know such impacts have occurred and need to
be included).
Hence, highlight these (dumrst, dumdp, dumdpl), set the lag
length option at
the bottom right-hand side of the window to 0 and then click on
'<Add'. Scroll
down the 'Model' window, and you will see that these dummies
have 'Y' next to

94. them, which indicates they will be modelled as additional
variables. Since we
only want them to enter unrestrictedly in the short-run model,
select/highlight
the dummies and then in the 'Status' options on the left-hand
side (the buttons
under 'Status' become available once a variable in the model is
highlighted)
click on 'Unrestricted', so that each dummy now has a 'U' next
to it in the
model.
Finally, on the right-hand side of the 'Data selection' window is
a
box headed 'Special'. These are the deterministic components
that can be
selected and added to the model. In this instance, we select
'CSeasonal
(centred seasonal dummies), as the data are seasonally
unadjusted, and
add the seasonal dummies to the model. They automatically
enter as unrest-
ricted. Note that if the time 'Trend' is added, it will not have a
'U' next to it
in the model, indicating it is restricted to enter the cointegration
space
(Model 4 in Chapter 5—see equation (5.6)). If we wanted to
select Model
2 then we would not enter the time trend (delete it from the
model if it is
already included), but would instead click on 'Constant' in the
'Model'
box and click on 'Clear' under the 'Status' options. Removing
the unrest-
ricted status of the constant will restrict it to enter the
cointegration space.

95. Thus, we can select Models 2–4, one at a time, and then decide
which
deterministic components should enter II, following the Pantula
principle
(see Chapter 5).
Having entered the model required, click OK, bringing up the
'Model
settings' window, accept the default of 'Unrestricted system' (by
clicking OK
again) and accept ordinary least squares (OLS) as the estimation
method
(again by clicking OK). The results of estimating the model will
be available
in Give Win (the 'Results' window—accessed by clicking on the
Give Win
toolbar on your Windows status bar). Return to the PcGive
window (click
on its toolbar), choose the 'Test' option to activate the drop-
down options,
and click on 'Test summary'. This produces the output in
GiveWin as shown in
Figure A.3. The model passes the various tests equation by
equation and by
using system-wide tests.
Several iterations of the above steps are likely to be needed in
practice to
obtain the lag length (k) for the VAR, which deterministic
components should
enter the model (i.e., any dummies or other 7(0) variables that
are needed in the
short-run part of the VECM to ensure the model passes the
diagnostic tests
on the residuals) and which deterministic components should
enter the

96. cointegration space (i.e., should the constant or trend be
restricted to be
included in II). To carry out the last part presumes you have
already tested
for the rank of II, so we turn to this next.
To undertake cointegration analysis of the I(1) system in
PcGive, choose
Test', then 'Dynamic Analysis and Cointegration tests' and
check the "7(1)
APPENDIX
rm
Y
dp
rstar
rm
Y
dp
rstar
rm
Y
dp
rstar
rm
y
dp
rstar
rm
y
dp
rstar

97. 263
Portmanteau(11):
Portmanteau(11) :
Portmanteau(11):
Portmanteau(11) :
AR 1-5 test:
AR 1-5 test:
AR 1-5 test:
AR 1-5 test:
Normality test:
Normality test:
Normality test:
Normality test:
ARCH 1-4 test:
ARCH 1-4 test:
ARCH 1-4 test:
ARCH 1-4 test:
hetero test:
hetero test:
hetero test:
hetero test:
11.2164
6.76376
3.66633
11.6639
F(5,
F(5,
F(5,
F(5,
Chi'
Chi-
Chi'
Chi'
F(4,

98. F(4,
F(4,
F(4,
F(35
F(35
F(35
F(35
73)
73)
73)
73)
2(2)
2(2)
2(2)
2(2)
70)
70)
70)
70)
,42)
,42)
,42)
,42)
1
1
1
1
2
5
4
o
— 1

99. = 1
-I
- 0.
= 0.
= 0.
= 0.
- 0.
.4131
.8569
.0269
.8359
.8297
.0521
.6973
.7019
.5882
.1669
.1133
68023
38980
72070
67314
88183

100. [0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
[0.
2297]
1125]
4083]
1164]
2430]
0800]
0955]
2590]
1871]
3329]
3573]
6080]
9974]
8385]
8838]
6463]
Vector Portmanteau(ll): 148.108
Vector AR 1-5 test: F(80,219)= 1.0155 [0.4555]

101. Vector Normality test: Chi'2(8) = 15.358 [0.0525]
Vector hetero test: F(350,346)= 0.47850 [1.0000]
Not enough observations for hetero-X test
Figure A.3. Estimating the unrestricted VAR in PcGive 10.1;
model diagnostics.
cointegration analysis' box.5 The results are produced in Figure
A.4,6 provid-
ing the eigenvalues of the system (and log-likelihoods for each
cointegration
rank), standard reduced rank test statistics and those adjusted
for degrees of
freedom (plus the significance levels for rejecting the various
null hypotheses)
and full-rank estimates of a, p and IT (the P are automatically
normalized along
the principal diagonal). Graphical analysis of the (J-vectors
(unadjusted and
adjusted for short-run dynamics) are available to provide a
visual test of which
vectors are stationary,7 and graphs of the recursive eigenvalues
associated with
each eigenvector can be plotted to consider the stability of the
cointegration
vectors.8
5 Note that the default output only produces the trace test. To
obtain the A-max test as
well as the default (and tests adjusted for degrees of freedom),
in PcGive choose 'Model',
then 'Options', 'Further options' and put a cross in the box for
cointegration test with
Max test.
6 Note that these differ from Box 5.5 and Table 5.5, since the
latter are based on a model

102. without the outlier dummies included in the unrestricted short-
run model.
7 The companion matrix that helps to verify the number of unit
roots at or close to
unity, corresponding to the 7(1) common trends, is available
when choosing the
'Dynamic analysis' option in the 'Test' model menu in PcGive.
8 Note that, to obtain recursive options, the 'recursive
estimation' option needs to be
selected when choosing OLS at the 'Estimation Model' window
when formulating the
model for estimation.
264 APPENDIX
1(1) cointegration analysis, 1964 (2) to 1989 (2)
eigenvalue
0.57076
0.11102
0.063096
0.0020654
loglik for rank
1235.302 0
1278.012 1
1283.955 2
1287.246 3
1287.350 4
rank Trace test [ Prob] Max test [ Prob] Trace test [T-nm] Max
test [T-nm]
0 104.10 [0.000]** 85.42 [0.000]** 87.61 [0.000]** 71.89
[0.000]'

103. 1 18.68 [0.527] 11.89 [0.571] 15.72 [0.737] 10.00 [0.747]
2 6.79 [0.608] 6.58 [0.547] 5.72 [0.731] 5.54 [0.676]
3 0.21 [0.648] 0.21 [0.648] 0.18 [0.675] 0.18 [0.675]
Asymptotic p-values based on: Unrestricted constant
Unrestricted variables:
[0] = Constant
[1] = CSeasonal
[2] = CSeasonal_l
[3] = CSeasonal_2
[4] = dumrst
[5] = dumdp
[6] = dumdp1
Number of lags used in the analysis: 4
beta (scaled on diagonal; cointegrating vectors in columns)
rm
y
dp
rstar
1.0000
-1.0337
6.4188
6.7976
15.719
1.0000
-207.49
131.02
-0.046843
0.064882
1.0000
-0.039555

104. 1.6502
-0.13051
8.6574
1.0000
alpha
rm -0.18373
y -0.0081691
dp 0.022631
rstar 0.0046324
0.00073499
-0.0010447
0.00023031
-0.0011461
0.0012372
-0.16551
-0.042258
-0.0022919
-0.0010530
-0.00080063
0.0010822
0.0018533
long-run matrix, rank 4
rm y
rm -0.17397 0.19088
y -0.018159 -0.0032342
dp 0.030017 -0.026047
rstar -0.010218 -0.0063252

105. dp
-1.3397
-0.0081182
0.064590
0.28129
rstar
-1.1537
-0.18666
0.18677
-0.11673
Figure A.4. 7(1) cointegration analysis in PcGive 10.1.
After deciding on the value of r < n, it is necessary to select a
reduced rank
system. In PcGive, under 'Model', choose 'Model settings' (not
'Formulate'),
select the option 'Cointegrated VAR' and in the window that
appears set the
cointegration rank (here we change '3' to '1', as the test
statistics indicate that
r — 1). Leave the 'No additional restrictions' option unchanged
as the default,
click OK in this window and the next, and the output (an
estimate of the new
value of II together with the reduced-form cointegration
vectors) will be
written to the results window in GiveWin.
Finally, we test for restrictions on a and p (recall that these
should usually
be conducted together). To illustrate the issue, the model
estimated in Chapter 6

106. APPENDIX , , 265
Figure A.5. Testing restrictions on a and B using 'General
Restrictions' in PcGive 10.1.
is chosen (instead of the one above) with a time trend restricted
into the
cointegration space and r — 2. Thus, we test the following
restrictions:
, r-i i * * o
[ 0 — 1 * * *
,_ r* o * o
~~ L* o * o
using the option 'General restrictions'. To do this in PcGive,
under 'Model',
choose 'Model settings', select the option 'Cointegrated VAR'
and in the
window that appears set the cointegration rank (here we change
'3' to '2',
since we have chosen r = 2). Click the 'General restrictions'
option, type the
relevant restrictions into the window (note that in the 'Model'
the parameters
are identified by '&' and a number—see Figure A.5), click OK
in this window
(and the next) and the results will be written into Give Win
(Figure A.6—see
also the top half of Box 6.1).
CONCLUSION

107. For the applied economist wishing to estimate cointegration
relations and then
to test for linear restrictions, PcGive 10.1 is a flexible option.
But there are
others. Harris (1995) compared three of the most popular
options available in
the 1990s (Microfit 3.0, Cats (in Rats) and PcFiml—the latter
the predecessor
to the current PcGive). The Cats program9 has seen little
development since its
9 Cointegration Analysis of Times Series (Cats in Rats), version
1.0, by Henrik Hansen
and Katrina Juselius, distributed by Estima.
266 APPENDIX
Cointegrated VAR (4) in:
[0] - rm
tl] = y
[2] = dp
[3] = rstar
Unrestricted variables:
[0] = dumrst
[1] = dumdp
[2] = dumdp 1
[3] = Constant
[4] = CSeasonal
[5] = CSeasonal_l
[6] = CSeasonal_2
Restricted variables:
[0] = Trend
Number of lags used in the analysis: 4
General cointegration restrictions:

108. &8=-l;&9=l;&12=0;
&13=0;&14=-1;
&2=0;&3=0;&6=0;&7=0;
beta
rm
y
dp
rstar
Trend
-1.0000
1.0000
-6.5414
-6.6572
0.00000
0.00000
-1.0000
2.8091
-1.1360
0.0066731
Standard errors of beta
rm
y
dp
rstar
Trend
alpha
rm
y
dp
rstar

109. 0.00000
0.00000
0.88785
0.33893
0.00000
0.17900
0.00000
-0.011637
0.00000
0.00000
0.00000
0.46671
0.19346
0.00020557
0.083003
0.00000
-0.15246
0.00000
Standard errors of alpha
rm 0.018588 0.074038
y 0.00000 0.00000
dp 0.0078017 0.031076
rstar 0.00000 0.00000
log—likelihood 1290.6274 -T/2log|Omega| 1863.87857
no. of observations 101
rank of long-run matrix 2
beta is identified
AIC -35.2253