I have two time series from (A) 1981-2010 and (B) 2011-2017. I noticed some change in the Time B but I do not know how to perform a test to say the change is statistically significant. I have performed Mann-Kendall in the entire time series and results show there is a trend. What I want to know if the change in Time B compared to the rest is significant.

This is the sample monthly data from 1981-2017. In the last seven years, there is a rise and I want to know if that is significant.

  • $\begingroup$ Can you add a lot more detail? What are the time series? Why do you need to test for a change? Change in what specifically (level, trend, variance, ...)? $\endgroup$ – The Laconic Apr 28 '18 at 13:34
  • $\begingroup$ Hi, I have monthly hurricane frequency count from 1981-2017 and I noticed an upward trend since 2011. I want to know if the change from last seven years is significant from the last 30 years. $\endgroup$ – user2543 Apr 28 '18 at 23:45
  • $\begingroup$ @TheLaconic: I added the data and answered your comment. $\endgroup$ – user2543 Apr 30 '18 at 0:34

Before you get to the mechanics of the test, there is an important issue you are overlooking. You say in the comments that you are testing this hypothesis (of a change in trend at 2011) because you noticed an upward trend in the data since 2011. Since you used your exploratory observations of the data to form your hypothesis, it is not valid to use that same data to test the hypothesis. The reason for this is that your hypothesis has been cherry-picked from exploratory analysis, precisely because you saw (visual) evidence of a change; if you use the same data to test it, that evidence will necessarily contribute to confirmation of the hypothesis, and this imposes an extremely strong confirmatory bias on the test. You would either need to find an independent testing data set (which is probably impossible) or else apply a more general test that does not pre-specify the time of the break according to your exploratory observations. In short, you should be testing a more general hypothesis that there is a change in trend at some point in the data.

The Mann-Kendall (MK) trend test is a non-parametric test that looks for a single trend in the data. It is not applicable to test the hypothesis of a changing trend. To do the latter you would need to formulate an appropriate time-series model that allows for multiple trend/drift terms over time. You could then test the hypothesis that there is only a single trend/drift term, against the hypothesis that there are multiple different trend/drift terms (at unspecified times). This would be a difficult custom-built model/test and it would require substantial expertise in statistics to design.

In future, if you only have one data set that you can use for testing, make sure you form all your hypotheses before you look at it!

  • $\begingroup$ Thanks. The first paragraph, I get it: it would be quite erroneous to deduce just from this dataset. But what should I do now, if I may ask? $\endgroup$ – user2543 Apr 30 '18 at 0:56
  • $\begingroup$ You will need to come up with a test that tests the general hypothesis "is there more than one trend with a break-point somewhere". This will probably require a custom model. $\endgroup$ – Ben Apr 30 '18 at 2:09
  • $\begingroup$ Okay. How do I do that? You are right: I came up with visual analysis in comparing two dataset, which reminds me, have you look into the dataset I attached in the question above? $\endgroup$ – user2543 Apr 30 '18 at 2:49

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