ADF Test Statistic
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-6.993069
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1% Critical Value*
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-3.4922
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5% Critical Value
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-2.8884
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10% Critical Value
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-2.5809
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*MacKinnon critical values for rejection of hypothesis of a unit root.
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Augmented Dickey-Fuller Test Equation
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Dependent Variable: D(Y)
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Method: Least Squares
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Sample(adjusted): 2 108
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Included observations: 107 after adjusting endpoints
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Variable
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Coefficient
|
Std. Error
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t-Statistic
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Prob.
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Y(-1)
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-0.630127
|
0.090107
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-6.993069
|
0.0000
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C
|
4.262106
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0.610344
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6.983121
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0.0000
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|
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R-squared
|
0.317752
|
Mean dependent var
|
-0.000982
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Adjusted R-squared
|
0.311255
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S.D. dependent var
|
0.371408
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S.E. of regression
|
0.308234
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Akaike info criterion
|
0.502601
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Sum squared resid
|
9.975877
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Schwarz criterion
|
0.552561
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Log likelihood
|
-24.88917
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F-statistic
|
48.90301
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Durbin-Watson stat
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2.091670
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Prob(F-statistic)
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0.000000
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Example 2: Case ST Revisited
Variable: Gross Domestic Product in billions of dollars, seasonally adjusted annual rate, quarterly. Divided by GDP Implicit Price Deflator, Index 2000=100
Range: 1960:1 to 2004:4
1. Ttimeplot of log
2. Unit Root Test Using
(a) Regression
Dependent Variable: D(Y)
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Sample (adjusted): 1960Q2 2004Q4
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Included observations: 179 after adjustments
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Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
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C
|
0.321734
|
0.142301
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2.260937
|
0.0250
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Y(-1)
|
-0.041774
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0.019072
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-2.190338
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0.0298
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QUARTER
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0.000319
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0.000152
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2.098769
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0.0373
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R-squared
|
0.032387
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Mean dependent var
|
0.008236
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Adjusted R-squared
|
0.021392
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S.D. dependent var
|
0.008588
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S.E. of regression
|
0.008495
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Akaike info criterion
|
-6.681989
|
Sum squared resid
|
0.012702
|
Schwarz criterion
|
-6.628569
|
Log likelihood
|
601.0380
|
F-statistic
|
2.945480
|
Durbin-Watson stat
|
1.386973
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Prob(F-statistic)
|
0.055174
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(b) Unit Root Test
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Null Hypothesis: Y has a unit root
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Exogenous: Constant, Linear Trend
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Lag Length: 0 (Fixed)
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t-Statistic
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Prob.*
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Augmented Dickey-Fuller test statistic
|
-2.190338
|
0.4916
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Test critical values:
|
1% level
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-4.010143
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5% level
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-3.435125
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10% level
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-3.141565
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*MacKinnon (1996) one-sided p-values.
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Augmented Dickey-Fuller Test Equation
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Dependent Variable: D(Y)
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Method: Least Squares
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Date: 05/06/05 Time: 11:27
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Sample (adjusted): 1960Q2 2004Q4
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Included observations: 179 after adjustments
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Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
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|
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|
Y(-1)
|
-0.041774
|
0.019072
|
-2.190338
|
0.0298
|
C
|
0.338664
|
0.150335
|
2.252734
|
0.0255
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@TREND(1960Q1)
|
0.000319
|
0.000152
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2.098769
|
0.0373
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R-squared
|
0.032387
|
Mean dependent var
|
0.008236
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Adjusted R-squared
|
0.021392
|
S.D. dependent var
|
0.008588
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S.E. of regression
|
0.008495
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Akaike info criterion
|
-6.681989
|
Sum squared resid
|
0.012702
|
Schwarz criterion
|
-6.628569
|
Log likelihood
|
601.0380
|
F-statistic
|
2.945480
|
Durbin-Watson stat
|
1.386973
|
Prob(F-statistic)
|
0.055174
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DW indicates autocorrelation in the residual. This could invalidate the test.
(c) Augmented Dickey – Fuller Test
For making the residual of the regression WN.
-
Null Hypothesis: Y has a unit root
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|
Exogenous: Constant, Linear Trend
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Lag Length: 1 (Fixed)
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t-Statistic
|
Prob.*
|
|
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|
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|
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Augmented Dickey-Fuller test statistic
|
-2.991965
|
0.1374
|
|
Test critical values:
|
1% level
|
|
-4.010440
|
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5% level
|
|
-3.435269
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10% level
|
|
-3.141649
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*MacKinnon (1996) one-sided p-values.
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|
Augmented Dickey-Fuller Test Equation
|
|
|
Dependent Variable: D(Y)
|
|
|
|
Method: Least Squares
|
|
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|
Date: 05/06/05 Time: 11:31
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|
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|
Sample (adjusted): 1960Q3 2004Q4
|
|
|
Included observations: 178 after adjustments
|
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Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
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|
|
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|
|
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|
|
Y(-1)
|
-0.054580
|
0.018242
|
-2.991965
|
0.0032
|
|
D(Y(-1))
|
0.308088
|
0.070503
|
4.369858
|
0.0000
|
|
C
|
0.437102
|
0.143758
|
3.040543
|
0.0027
|
|
@TREND(1960Q1)
|
0.000422
|
0.000145
|
2.901395
|
0.0042
|
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|
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|
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|
R-squared
|
0.136809
|
Mean dependent var
|
0.008310
|
|
Adjusted R-squared
|
0.121926
|
S.D. dependent var
|
0.008554
|
|
S.E. of regression
|
0.008015
|
Akaike info criterion
|
-6.792672
|
|
Sum squared resid
|
0.011179
|
Schwarz criterion
|
-6.721171
|
|
Log likelihood
|
608.5478
|
F-statistic
|
9.192547
|
|
Durbin-Watson stat
|
2.146510
|
Prob(F-statistic)
|
0.000011
|
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