Phillips–Perron unit root test instead of ADF test? I have read that PP unit root is often used in economy. Is it sensible to do both tests (PP & ADF) or is PP test enough?
 A: Generally, Adf test is used when the errors are homoscedastic and PP test is preferred for hetroscedastic errors.
A: A great advantage of Philips-Perron test is that it is non-parametric, i.e. it does not require to select the level of serial correlation as in ADF. It rather takes the same estimation scheme as in DF test, but corrects the statistic to conduct for autocorrelations and heteroscedasticity (HAC type corrections).
The main disadvantage of the PP test is that it is based on asymptotic theory. Therefore it works well only in large samples that are indeed luxury if not it comes for financial time series data. And it also shares disadvantages of ADF tests: sensitivity to structural breaks, poor small sample power too often resulting in unit root conclusions.
It is advisable to make several tests and see if the results match, if not check the properties of the time series (PP is more robust to deviations from "gentleman's" set of properties!). You may also consider Zivot-Andrew test if you believe the data has structural breaks.
I have found this lecture notes Unit Root Testing To Help Model Building by L. Mahadeva and P.Robinson useful to answer the questions. May be it will give more information to you.
