Detrending or Differencing in order to make a series stationary?

I got several time series for which I want to find out if they are stationary or not. So I computed for each series the kpss.test(). But before making further calculations with my time series I wanted to make sure if I specified and interpret the ADF test correctly. My data are daily data (i.e. per week I have 5 observations).

First I computed the following ADF test. kpss.test(abx, c("Level")) for which I get the following result:

KPSS Test for Level Stationarity
data:  abx
KPSS Level = 1.0225, Truncation lag parameter = 4, p-value = 0.01

since the p-value is smaller than my critical value of 5% I can reject the null hypothesis that my series is stationary in levels?

Second I computed the following ADF test: kpss.test(abx, c("Trend") which gives me the following result:

KPSS Test for Trend Stationarity
data:  abx
KPSS Trend = 0.1544, Truncation lag parameter = 4, p-value = 0.04303

since this p- value is also smaller than my critical value of 5% I can reject the hypothesis that my series is stationary around a trend?

Now my conclusion from those two tests is: Since I can reject both hypothesis I can assume that my series is not trend stationary and not level stationary. This means it has a stochastic trend and in order to make it stationary I need to take the first difference. Is my conlusion here correct?

More general: By simply looking at the results from the first test one does not know if the series has a deterministic or/ and a stochastic trend. So that is why you also have to perform the second test in order to make sure if detrending or differencing is the right way to make the series stationary?

Another question I have: Is it possible to make the same conclusion (in case the one stated above is correct) using the following command ur.df() from the package urca?

Many thanks for your answers and opinions

• ADF test is not the same as KPSS test. The null hypothesis of KPSS test is stationarity, while the null hypothesis of ADF test is integratedness. – Richard Hardy Mar 24 '15 at 18:31
• many thanks for your answer. I just read the content from the following link: stats.stackexchange.com/questions/30569/… , but what about my conclusion about differencing my time series? – Michael B Mar 24 '15 at 18:50
• Your KPSS test results indicate that the series is non-stationary. Try ur.df as an extra test. If the null hypothesis in ur.df is not rejected, you will have extra evidence that your series is integrated. – Richard Hardy Mar 24 '15 at 19:04