# KPSS: Difference between level stationary and trend stationary

Can anyone please clarify for me the differences between level stationary and trend stationary in KPSS test? I run the KPSS test with trend and level on same time series and the results are:

H0: level stationary vs. H1: Unit root. Test statistic: 0.1691746

p-value: 0.245586 Upper tail percentiles: 10% 5% 2.5% 1% Critical value 0.347 0.463 0.573 0.739

## from above I infer level stationary at 5% as p-value>0.05 and test stat < 0.463.

H0: trend stationary vs. H1: Unit root. Test statistic: 0.08118887

p-value: 0.2409267 Upper tail percentiles: 10% 5% 2.5% 1% Critical value 0.119 0.146 0.176 0.216

## Here I accept the H0 and infer trend stationary at 5% (stationary around a deterministic trend)

1)I am not sure how to explain these two results? Is it stationary or should I de-trend my time series to make it stationary? 2) How come the second test accepts trend stationary when the p-value from MK test (mann kendall, where H0 is monotonic trend) is less than 0.01? I appreciate your advise.

I think you have a missunderstanding of the interpretation of a statistical test. In detail, you cannot conclude anything if the null hypothesis is not rejected. Especially you never accept $$H_0$$. You are just only able to "fail to reject $$H_0$$".
• @Saraz you are welcome. I don't really get what you mean with "at least one of them is not zero". The first interpretation of the test would be that your time series contains no unit root and is therefore trend stationary on a 1 % significance level (since $-22.591<-3.96$), i.e. is stationary except a deterministic trend. Additional you might want to test if your time series is even level stationary. In order to do so, you apply an ADF test with level and without trend. If you still can reject the null hypothesis of a unit root, you conclude stationarity. – FeynmanBestMan Jun 2 at 9:13