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Tue dole of National Bank of Rwanda from 1995 to 2010

( Télécharger le fichier original )
par Paterne RUKUNDO
National university of Rwanda - A0 2011
  

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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.

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