Appendix
Three types of Unit Root Test
For each test:
(a) Understand both H0 and H1.
(b) Learn how to implement:
To be able to specify the correct regression
To augment the regression when is not WN. (DW could tell)
Add Y(t-1) , Y(t-2), etc.
How To Select Proper Unit Root Test?
Personal opinion
Note the model of the alternative H1. -> test can be easily rejected.
If the first difference has clearly non-zero mean, then choose test.
If the mean of the first difference is close to 0, then try both and tests.
The following is not complete
The nature of the variable precludes the existence of a unit root.
In the absence of a unit root, the most plausible process is AR(2) with non-zero mean.
Model:
Rewriting for test:
=
=
Hypotheses:
H0: (AR(1) in the first difference)
H1: (Stationary AR(2) process)
Test Using Regression:
Dependent Variable: D(Y)
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Method: Least Squares
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Sample(adjusted): 3 108
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Included observations: 106 after adjusting endpoints
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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C
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1.308143
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0.366499
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3.569297
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0.0005
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Y(-1)
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-0.313898
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0.087968
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-3.568333
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0.0005
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D(Y(-1))
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-0.211258
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0.097010
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-2.177693
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0.0317
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R-squared
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0.233052
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Mean dependent var
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0.003104
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Adjusted R-squared
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0.218160
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S.D. dependent var
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0.362739
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S.E. of regression
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0.320740
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Akaike info criterion
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0.591520
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Sum squared resid
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10.59602
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Schwarz criterion
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0.666901
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Log likelihood
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-28.35057
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F-statistic
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15.64928
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Durbin-Watson stat
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1.993541
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Prob(F-statistic)
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0.000001
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