I'm using R to calculate the KPSS to check the stationarity.

The library that I'm using is tseries and the function is kpss.test

I have done a simple test using cars (a default matrix on R). The code is:

> k <- kpss.test(cars$dist, null="Trend")
Warning message:
In kpss.test(cars$dist, null = "Trend") :
  p-value greater than printed p-value
> k    
        KPSS Test for Trend Stationarity

data:  cars$dist 
KPSS Trend = 0.0859, Truncation lag parameter = 1, p-value = 0.1

> k$statistic
KPSS Trend 

> k$parameter
Truncation lag parameter 
> k$p.value
[1] 0.1

> k$method
[1] "KPSS Test for Trend Stationarity"

> k$data.name
[1] "cars$dist"

Those are all the results that kpss returns.

My question is: How to interpret them to understand if it is stationary?

Thank you in advance!


1 Answer 1


You specified a null hypothesis of trend stationarity. That is the data follow a straight line time trend with stationary errors. The p-value is 0.1, so the null hypothesis is not rejected at the usual 5% level.

  • $\begingroup$ I could translate your answer as: IF p-value is ABOVE 0.05 the trend is stationary otherwise NOT, correct? $\endgroup$
    – Dail
    Jul 19, 2011 at 8:32
  • 2
    $\begingroup$ A trend cannot be stationary. The null hypothesis is a time trend with stationary errors, as I explained. $\endgroup$ Jul 19, 2011 at 10:15
  • $\begingroup$ yes, excuse me: I meant a time trend with stationary errors. by the way, if the p-value is ABOVE 0.05 it means that is mean reverting (Stationary) right? $\endgroup$
    – Dail
    Jul 19, 2011 at 10:32
  • $\begingroup$ Assuming you are using the 5% level, then a p-value above 0.05 means you have no evidence that it is not trend stationary. That is not the same as saying that it is trend stationary. $\endgroup$ Jul 20, 2011 at 0:28
  • 3
    $\begingroup$ Trend stationary means "stationary around the trend", i.e. the trend needn't be stationary, but the de-trended data is. Level stationary means that the data is like white noise. $\endgroup$
    – SiKiHe
    May 22, 2015 at 7:24

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