4.6. Test for
stationary
The footstep of this analysis is to determine whether the
series are stationary or not. The ADF was used to test for stationary of these
series as it provides a superior test to DF, especially in case the residuals
of the regression could be serially correlated. The lag length has been
automatically selected by AIC from eleven proposed lags and all three
possibilities have been tested: neither intercept nor trend, intercept but no
trend and both intercept and trend.
TABLE 4.1: Money Stock
stationary (MT)
|
ADF Test Statistic
|
5.023678
|
1% Critical Value*
|
-2.7411
|
|
|
5% Critical Value
|
-1.9658
|
|
|
10% Critical Value
|
-1.6277
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(MT)
|
|
Method: Least Squares
|
|
Date: 07/20/11 Time: 09:07
|
|
Sample(adjusted): 1996 2010
|
|
Included observations: 15 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
MT(-1)
|
0.159544
|
0.031758
|
5.023678
|
0.0002
|
|
R-squared
|
0.322881
|
Mean dependent var
|
30.25333
|
|
Adjusted R-squared
|
0.322881
|
S.D. dependent var
|
33.05061
|
|
S.E. of regression
|
27.19644
|
Akaike info criterion
|
9.508390
|
|
Sum squared resid
|
10355.05
|
Schwarz criterion
|
9.555593
|
|
Log likelihood
|
-70.31292
|
Durbin-Watson stat
|
1.871053
|
As /ADF/ is greater than /5%/
critical value, MT is stationary at lag 0, level and function
of none.
TABLE 4.2: Inflation Gap
stationary (IG)
|
ADF Test Statistic
|
-4.663015
|
1% Critical Value*
|
-4.0113
|
|
|
5% Critical Value
|
-3.1003
|
|
|
10% Critical Value
|
-2.6927
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(IG)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 11:40
|
|
Sample(adjusted): 1997 2010
|
|
Included observations: 14 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
IG(-1)
|
-2.059676
|
0.441705
|
-4.663015
|
0.0007
|
|
D(IG(-1))
|
0.347099
|
0.247617
|
1.401760
|
0.1886
|
|
C
|
-1.341209
|
1.262206
|
-1.062591
|
0.3107
|
|
R-squared
|
0.796606
|
Mean dependent var
|
-0.105357
|
|
Adjusted R-squared
|
0.759626
|
S.D. dependent var
|
9.320982
|
|
S.E. of regression
|
4.569890
|
Akaike info criterion
|
6.064265
|
|
Sum squared resid
|
229.7229
|
Schwarz criterion
|
6.201206
|
|
Log likelihood
|
-39.44985
|
F-statistic
|
21.54115
|
|
Durbin-Watson stat
|
1.603652
|
Prob(F-statistic)
|
0.000157
|
As /ADF/ is greater than all
critical values especially /5%/, IG is stationary at lag 1,
level and function with intercept.
Table 4.3: Output Gap
stationary
|
ADF Test Statistic
|
-4.887496
|
1% Critical Value*
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(YG,3)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 12:11
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
D(YG(-1),2)
|
-2.449332
|
0.501143
|
-4.887496
|
0.0009
|
|
D(YG(-1),3)
|
0.595279
|
0.284900
|
2.089433
|
0.0662
|
|
C
|
-1.073325
|
9.702328
|
-0.110626
|
0.9143
|
|
R-squared
|
0.832995
|
Mean dependent var
|
-4.231833
|
|
Adjusted R-squared
|
0.795882
|
S.D. dependent var
|
74.27310
|
|
S.E. of regression
|
33.55613
|
Akaike info criterion
|
10.07663
|
|
Sum squared resid
|
10134.12
|
Schwarz criterion
|
10.19786
|
|
Log likelihood
|
-57.45980
|
F-statistic
|
22.44524
|
|
Durbin-Watson stat
|
1.843834
|
Prob(F-statistic)
|
0.000318
|
As /ADF/ is
greater than all critical values especially /5%/, YG is
stationary at lag 1, second difference and function with intercept.
TABLE 4.4: Variation of
Exchange stationary
|
ADF Test Statistic
|
-4.393650
|
1% Critical Value
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(DEXCH,3)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 12:16
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
D(DEXCH(-1),2)
|
-1.616566
|
0.367932
|
-4.393650
|
0.0013
|
|
C
|
17.89631
|
23.68642
|
0.755552
|
0.4673
|
|
R-squared
|
0.658752
|
Mean dependent var
|
14.17417
|
|
Adjusted R-squared
|
0.624627
|
S.D. dependent var
|
133.8383
|
|
S.E. of regression
|
81.99966
|
Akaike info criterion
|
11.80232
|
|
Sum squared resid
|
67239.43
|
Schwarz criterion
|
11.88314
|
|
Log likelihood
|
-68.81391
|
F-statistic
|
19.30416
|
|
Durbin-Watson stat
|
1.534741
|
Prob(F-statistic)
|
0.001348
|
As /ADF/ is
greater than all critical values especially /5%/, DEXCH is
stationary at lag 0, second difference and function with intercept.
TABLE 4.5: Previous Money
Stock stationary
|
ADF Test Statistic
|
-3.699480
|
1% Critical Value*
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(M1,3)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 12:20
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
D(M1(-1),2)
|
-1.159214
|
0.313345
|
-3.699480
|
0.0041
|
|
C
|
0.034242
|
8.436719
|
0.004059
|
0.9968
|
|
R-squared
|
0.577812
|
Mean dependent var
|
0.391667
|
|
Adjusted R-squared
|
0.535594
|
S.D. dependent var
|
42.88315
|
|
S.E. of regression
|
29.22374
|
Akaike info criterion
|
9.738851
|
|
Sum squared resid
|
8540.268
|
Schwarz criterion
|
9.819669
|
|
Log likelihood
|
-56.43311
|
F-statistic
|
13.68615
|
|
Durbin-Watson stat
|
2.076159
|
Prob(F-statistic)
|
0.004112
|
As / ADF/ is greater than / 5%/
critical value, M1 is stationary at lag 0, second difference
and function with intercept.
TABLE 4.6: Previous Inflation
Gap stationary
|
ADF Test Statistic
|
-4.663015
|
1% Critical Value*
|
-4.0113
|
|
|
5% Critical Value
|
-3.1003
|
|
|
10% Critical Value
|
-2.6927
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(IG)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 11:40
|
|
Sample(adjusted): 1997 2010
|
|
Included observations: 14 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
IG(-1)
|
-2.059676
|
0.441705
|
-4.663015
|
0.0007
|
|
D(IG(-1))
|
0.347099
|
0.247617
|
1.401760
|
0.1886
|
|
C
|
-1.341209
|
1.262206
|
-1.062591
|
0.3107
|
|
R-squared
|
0.796606
|
Mean dependent var
|
0.105357
|
|
Adjusted R-squared
|
0.759626
|
S.D. dependent var
|
9.320982
|
|
S.E. of regression
|
4.569890
|
Akaike info criterion
|
6.064265
|
|
Sum squared resid
|
229.7229
|
Schwarz criterion
|
6.201206
|
|
Log likelihood
|
-39.44985
|
F-statistic
|
21.54115
|
|
Durbin-Watson stat
|
1.603652
|
Prob(F-statistic)
|
0.000157
|
As /ADF/ is
greater than all critical values especially /5%/, IG1 is
stationary at lag 1, level and function with intercept.
Table 4.7: previous Output
Gap stationary
|
ADF Test Statistic
|
-5.810852
|
1% Critical Value*
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(YG1,3)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 12:27
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
D(YG1(-1),2)
|
-1.539314
|
0.264903
|
-5.810852
|
0.0002
|
|
C
|
1.842228
|
10.71345
|
0.171955
|
0.8669
|
|
R-squared
|
0.771512
|
Mean dependent var
|
0.864250
|
|
Adjusted R-squared
|
0.748663
|
S.D. dependent var
|
74.01819
|
|
S.E. of regression
|
37.10790
|
Akaike info criterion
|
10.21655
|
|
Sum squared resid
|
13769.96
|
Schwarz criterion
|
10.29737
|
|
Log likelihood
|
-59.29929
|
F-statistic
|
33.76600
|
|
Durbin-Watson stat
|
2.583075
|
Prob(F-statistic)
|
0.000170
|
As /ADF/ is greater than all
critical values especially /5%/, YG1 is stationary at lag 0,
second difference and function with intercept.
Table 4.8: Previous Variation
of Exchange stationary
|
ADF Test Statistic
|
-5.187147
|
1% Critical Value*
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(DEXCH1,2)
|
|
Method: Least Squares
|
|
Date: 09/19/11 Time: 12:36
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
D(DEXCH1(-1))
|
-1.469962
|
0.283386
|
-5.187147
|
0.0004
|
|
C
|
1.485446
|
10.59132
|
0.140251
|
0.8912
|
|
R-squared
|
0.729045
|
Mean dependent var
|
2.302500
|
|
Adjusted R-squared
|
0.701949
|
S.D. dependent var
|
67.19665
|
|
S.E. of regression
|
36.68534
|
Akaike info criterion
|
10.19364
|
|
Sum squared resid
|
13458.14
|
Schwarz criterion
|
10.27446
|
|
Log likelihood
|
-59.16186
|
F-statistic
|
26.90649
|
|
Durbin-Watson stat
|
2.085680
|
Prob(F-statistic)
|
0.000409
|
As /ADF/ is greater than all
critical value /5%/, DEXCH1 is stationary at lag 0, first
difference and function with intercept.
Table 4.9: Error Term
stationary
|
ADF Test Statistic
|
-4.335477
|
1% Critical Value*
|
-4.1366
|
|
|
5% Critical Value
|
-3.1483
|
|
|
10% Critical Value
|
-2.7180
|
|
*MacKinnon critical values for rejection of hypothesis of a unit
root.
|
|
|
|
|
|
|
|
|
|
|
|
Augmented Dickey-Fuller Test Equation
|
|
Dependent Variable: D(E)
|
|
Method: Least Squares
|
|
Date: 07/20/11 Time: 09:46
|
|
Sample(adjusted): 1999 2010
|
|
Included observations: 12 after adjusting endpoints
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
E(-1)
|
-1.299467
|
0.299729
|
-4.335477
|
0.0015
|
|
C
|
16.62786
|
9.471546
|
1.755559
|
0.1097
|
|
R-squared
|
0.652734
|
Mean dependent var
|
1.986182
|
|
Adjusted R-squared
|
0.618007
|
S.D. dependent var
|
49.59723
|
|
S.E. of regression
|
30.65385
|
Akaike info criterion
|
9.834405
|
|
Sum squared resid
|
9396.583
|
Schwarz criterion
|
9.915223
|
|
Log likelihood
|
-57.00643
|
F-statistic
|
18.79636
|
|
Durbin-Watson stat
|
1.976710
|
Prob(F-statistic)
|
0.001477
|
As /ADF/ is
greater than /5%/ critical value, error term is stationary at 0 lag, level and
function with intercept.
Notes: all tests of stationary are done in Eviews 3.1
CUSUM TEST
Source of basic data: BNR, NISR and MINECOFIN
As the line of cusum does not get out of the corridor, means that
the parameters of the regression model are stable.
M = 48.62344 + 0.996100M1 + 1.492988IG + 2.824734IG1 - 0.549954YG
+ 0.099609YG1 -
P (0.001) (0.003) (0.002)
(0.000) (0.02) (0.007)
0.088485EX - 0.311933EX1.
(0.0045) (0.01)
F table = 4.7 Fcritical =
38.02
R2 = 0.98 dw = 2.46
As dw is greater than R2, the estimated model is
correctly specified.
DW and BREUCH-GODFREY TEST show that there is no autocorrelation
because the
DW is the zone of none autocorrelation zone and nR2
> ÷2 for LM (Lagrangian Multiplier or
Breuch-Godfrey Test)
nR2=31.36 > X2 =9.88623
R2 is coming from estimation of errors.
All coefficients have an econometric sense explained by
Fcritical that is greater than Ftable , means that the
concerned variables have an effect on current money stock aggregate.
After testing stationary for all variables and model
specification, now interpretation.
| 
