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Question 1

Explain the rationale for the ADF test? What is it’s solution?

Answer 1

The DF test is only valid if u(t) is white noise

u(t) will be autocorrected if there was autocorrelation in the dependent variable (change in y(t))

Solution: augment the test using p lags of the dependent variable

Question 2

What does the ADF alternative model now become?

Answer 2

Same as before but with an added term

Sum(alpha(i).changey(t-i))
For i=1 to p

Same CVs

Question 3

What problem then arises with the ADF test? 2 solutions?

Answer 3

Problem arises in determining the optimal number of lags of dependent variable:
Can use 2 ways to decide:
- frequency of data
- information criteria

Question 4

What is the Phillips-Peron test?

Answer 4

Similar to ADF test except it incorporates an automatic correlation to allow for autocorrected residuals

Question 5

Main criticism to PP and DF tests?

Answer 5

Power of tests is low if process is stationary but has a roof close to the non stationary boundary (ie. 0.95)

Question 6

Main solution to low test power for DF and PP tests?

Answer 6

Use a stationarity test (ie. KPSS) as well;

H0: stationarity
H1: non-stationarity