I have a time series consisting of 192 data points (12 years of monthly data). A simple plot (in my opinion) clearly indicates that the data are not stationary:

enter image description here

However, when I do an ADF test I get a contradictive result:

    Augmented Dickey-Fuller Test

data:  Holidays
Dickey-Fuller = -6.0611, Lag order = 5, p-value = 0.01
alternative hypothesis: stationary

To make it even more confusing I also did a KPSS and PP test which gave following results:

    KPSS Test for Trend Stationarity

data:  Holidays
KPSS Trend = 0.28421, Truncation lag parameter = 3, p-value = 0.01

    Phillips-Perron Unit Root Test

data:  Holidays
Dickey-Fuller = -10.166, Truncation lag parameter = 4, p-value = 0.01

So basically the plot and KPSS test (both trend and level stationarity were tested) are in favor of non-stationarity, while the ADF test and PP test indicate the series is stationary.

I am confused now. Which test should I believe and how can they be contradictive?

  • $\begingroup$ Strongly related question maybe even duplicate? $\endgroup$ – Joel May 15 '18 at 13:55

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