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I need to check second order stationarity of a time series of length 7320 (I have 1800 such time series). These time series are displacement recorded at 1800 sites on a mountain. I tried using Priestley-Subba Rao in R : stationarity(). For 1 time series out of 1800, I got these values:

p-value for T : 2.109424e-15 
p-value for I+R : 9.447661e-06 
p-value for T+I+R : 1.4099e-10

Could you please tell me how to interpret it. All I know is if the p-value for T is 0, the null hypothesis of time series being stationary is rejected. Also, for 2nd time series out of 1800, I got these values;

p-value for T : 0 
p-value for I+R : 1.458063e-09 
p-value for T+I+R : 0

Could you tell me how to differentiate between the two. Both the time series are from the same dataset. Also, is it possible that one time series is stationary and another is not, given the fact they are from the same site and recorded at the exact same time.

I also tried Wavelet Spectrum Test in R: hwtos2() function. But this function takes the time-series length that are power of 2. Is there any other better test for looking at stationarity that does not limit with the length of time series?

Kevin Arseneau
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Nitika Kandhari
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    If your question relates to whether or not the code you used to generate the result contains a problem, please edit and provide a [minimal reproducible example](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example). Otherwise, to ask about the interpretation of your results, that may be better asked on [Cross Validated](https://stats.stackexchange.com/). – Kevin Arseneau Jan 29 '18 at 05:44

1 Answers1

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The book "Nonstationarities in Hydrologic and Environmental Time Series" (Springer Ed.), at pag. 119, provides a good explanation for interpreting those p-values within the Priestley-Subba Rao test.

In general, you may also take a look at:

https://www.stat.tamu.edu/~suhasini/test_papers/priestley_subbarao70.pdf

About other stationarity tests, you may have a look at "weakly.stationary()" function within "analytics" package and to the "costat" package whose info at:

https://www.jstatsoft.org/article/view/v055i01

where there is a suggestion to handle non dyadic length (i.e., 2^J for some natural number J) time series. At pag. 5:

"It should be made clear that this is not a limitation of wavelets per se, but of the computationally efficient algorithms used to compute the intended quantities. Data sets of other lengths can be handled by zero-padding or truncation"

Some interesting info at:

https://arxiv.org/pdf/1603.06415.pdf

GiorgioG
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