I have a time series data for 18 months. To check for stationary I conducted adf test, to which my p value is 0.8. And kpss test has a p value of 0.1 , so at 95% confidence level I fail to reject null in both cases. That means my adf test confirm that data is non stationary whereas kpss test confirms my data as stationary. Why is that happening?
For the data you have, neither test is powerful enough to reject the null hypothesis. But it looks like KPSS test is not too far from rejecting it; a little more power (a little more data), and that might have happened. If so, the results of the ADF and KPSS tests would not be contradictory anymore. So I do not see a big disagreement in the test results in your application.