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

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


What does the ADF alternative model now become?

Same as before but with an added term

For i=1 to p

Same CVs


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

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


What is the Phillips-Peron test?

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


Main criticism to PP and DF tests?

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


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

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

H0: stationarity
H1: non-stationarity