I have a wait-time time series for 10 weekdays(2 weeks) with 10 minutes intervals. I'm having hard time to interpret this? Is this stationary? I also applied Philips-Perron Unit root test and I got the following values. Any help is appreciated.

Dickey-Fuller = -8.4726, Truncation lag parameter = 5, p-value = 0.01

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  • $\begingroup$ What is the null hypothesis of the dickey fuller test, and what are the critical values? $\endgroup$ – fredrikhs Nov 10 '13 at 14:20
  • $\begingroup$ I use PP.test function of R. I believe the null hypothesis is being non-stationary, but I might be wrong. $\endgroup$ – fatih Nov 10 '13 at 14:38
  • $\begingroup$ In the description of the function it says that it is a test for the null hypothesis that x has a unit root against a stationary alternative. How do you interpret the p-value then? $\endgroup$ – fredrikhs Nov 10 '13 at 14:54
  • $\begingroup$ Then I assume, I should reject the null hypothesis, because the p-value is less than significant boundary (0.05). So the series is stationary. Correct? $\endgroup$ – fatih Nov 10 '13 at 15:01
  • 1
    $\begingroup$ That is correct. $\endgroup$ – fredrikhs Nov 10 '13 at 15:03

Both visually and statistically your time series is very stationary. It looked like you used the Augmented Dickey Fuller (ADF) test to test whether your time series is stationary and it is. Several of the unit root test testing for stationarity have similar parameters associated with a tau statistics (similar to a t stat). And, you want the tau statistics to be very negative, meaning that your time series mean-reverts (in the opposite direction of the previous change) very quickly.

In conjunction with a very negative tau statistics, you want an associated very low P value at least less than 0.05. This indicates that this variable does mean revert very quickly, and that there is a very small chance (0.05) that it does that purely by chance.

In your case, with a t stat of -8.5 and a P value < 0.01, you can be sure that this time series is stationary. You can clearly see that visually as the line zig zags up and down very quickly. It does not trend in the same direction for long.


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