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!

The series

  • $\begingroup$ Well it clearly looks like that around 83-85 the trend changes. If you were to perform linear regression (which you shouldn't, but if you WERE), then you'd most definitely do it piecewise. Try running the tests for the two different time intervals $\endgroup$ – Lagerbaer Jan 10 '17 at 21:48
  • $\begingroup$ If this is a time series, the apparent large trend indicates nonstationarity. If you are interested in removing the trend to make the series stationary you would not use a linear trend, piecewise linear as Lagerbaer suggests or quadratic. $\endgroup$ – Michael Chernick Jan 10 '17 at 22:46
  • $\begingroup$ The curve is puzzling because the curve is so smooth and the axes are not clearly explained. $\endgroup$ – Michael Chernick Jan 10 '17 at 22:49
  • $\begingroup$ Thanks for the help so far! The x-axis represents the year (as in 80=1980), the y-axis shows the level of LHICP. I have performed the tests on the two different intervals seperately and now both tests reject the null for all specifications. Can i now safely conclude the series is I(1)? $\endgroup$ – user144885 Jan 10 '17 at 23:00
  • $\begingroup$ Price index is an accumulation of many increments. Try the first difference or the percentage change. Sidenote: PI are long memory process in my experience. $\endgroup$ – mugen Jan 11 '17 at 2:56

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