Case u rt1: Unit Root Tests – More Examples



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Appendix


  1. 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.



  1. How To Select Proper Unit Root Test?

    Personal opinion





  1. Note the model of the alternative H1. ->  test can be easily rejected.



  2. 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


    1. The nature of the variable precludes the existence of a unit root.

    2. 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)

Method: Least Squares

Sample(adjusted): 3 108

Included observations: 106 after adjusting endpoints

Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.308143

0.366499

3.569297

0.0005

Y(-1)

-0.313898

0.087968

-3.568333

0.0005

D(Y(-1))

-0.211258

0.097010

-2.177693

0.0317

R-squared

0.233052

Mean dependent var

0.003104

Adjusted R-squared

0.218160

S.D. dependent var

0.362739

S.E. of regression

0.320740

Akaike info criterion

0.591520

Sum squared resid

10.59602

Schwarz criterion

0.666901

Log likelihood

-28.35057

F-statistic

15.64928

Durbin-Watson stat

1.993541

Prob(F-statistic)

0.000001

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