In order to correctly estimate a VAR model, i have to determine whether my variable, the log of the Harmonized Index of Consumer Prices, is stationary. Now, I have performed both the ADF and the PP tests. The ADF-test rejects the null hypothesis with every specification (trend+constant, constant, nothing). However, the trend coefficient is not significant which should disprove a deterministic trend. The PP test does not reject the null when a trend is included, and rejects the null when there is no trend included. My confusion stems from the graph of the series as it obviously shows a trend. My intuition says the series should be I(1), but the tests say otherwise. How do i correctly determine the order of integration in this situation?
Thanks in advance!