Hello!
After reading several websites, i still can't be 100% sure when chosing between none, Intercept only, Trend only and both (trend and inercept) for unit root testing. So, i will really appreciate any suggestion when choosing between the models mentioned above, especialy when working with the next tests:
- ADF
- Phillips - Perron
- Kpss
- Zivot - Andrews
looking forward to your help.
Regards,
Joel
Dear Nip,
You should try all the cases: none, intercept, intercept and trend. A variable is stationary even if one of the cases shows that.
Zivot and Andrews unit root test is used only in the case that your series-variable has structural brake. More specifically, Zivot and Andrews (1992) endogenous structural break test is a sequential test which utilizes the full sample and uses a different dummy variable for each possible break date. The break date is selected where the t-statistic from the ADF test of unit root is at a minimum (most negative). Consequently a break date will be chosen where the evidence is least favorable for the unit root null. The critical values in Zivot and Andrews (1992) are different to the critical values in Perron (1989). The difference is due to that the selecting of the time of the break is treated as the outcome of an estimation procedure, rather than predetermined exogenously
Now, regarding your question, if u want to be 100 % sure then you have to implement all the tests (apart from this of Zivot and Andrews) with all the kinds of their specifications. However, KPSS-type tests are intended to complement unit root tests, such as the Dickey–Fuller tests. So, by testing your variables with adf and pp tests you will be ok and in the case that you are not sure for the results then turn your attention to the KPSS type results (since it is a complementary test)
Dear my friend,
There are several tests examining unit root in the variables. But generally,ADF and PP tests are applied in the case of time series models.
Yours.
Unit root tests are known to have low power. It is, therefore important that you choose the correct test. I would advise that you use economics or common sense or some other knowledge of the series that you are examining. As you state there are three tests (1) no constant and no trend, (2) constant and no trend and (3) constant and trend. The choice of test depends on the alternative to your I(1) hypothesis. For example if you assumed that the alternative was stationary with zero mean you would use (1). If you assumed that the alternative was stationary about some constant you would use test (2). An example would be a real exchange rate or some other return on an asset. Such a variable is unlikely to be trending so one would not include a trend in the alternative. If you are looking at a variable like gdp or cpi then they are trending and one would use (3)
I would also recommend that you use one of the more powerful versions of the adf test (e.g. DF-GLS test) rather than the standard adf or pp tests.
Nip Nip
I have only just seen your comment about a minimum sample of 50 for the DF-GLS (ERS) unit root test. It is relatively easy to estimate critical values for smaller sample sizes. The methodology for this is described in Chapter 17 of Martin, Hurn and Harris (2013), Econometric Modelling with time series, Cambridge University Press.
http://www.cambridge.org/features/econmodelling/ the companion web sit for the book has programs in matlab, R and Gauss to estimate the critical values.
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