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I am new to time series data analysis. I wonder how would one test the difference between integrated quantities (area under curve) from different time-series curves? (the time series are plotted with biweekly GHG flux data, the flux data has standard error associated with it). Like comparing cumulative/annual total greenhouse gas emission in different geographical regions. Thank you very much.

y chung
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  • What do you mean by "test the difference". You can just compare the integrated values. Or you mean to test if the differences are statistically significant?? I find the question unclear, please explain better your problem. – Camilo Rada Apr 03 '19 at 17:09
  • Yes, I mean testing the statistical significance of the difference – y chung Apr 03 '19 at 17:45
  • Do you know the error associated with each data point? – Camilo Rada Apr 03 '19 at 18:12
  • Yes, I have standard error of each GHG flux data point – y chung Apr 03 '19 at 20:12
  • One way to go about it is to compute the p-value. That is: if one cumulative GHG emission is A and other is B. And you have that the value you get for A is greater then B. You take the null hypothesis that A=B, and given the errors of the data, the p-value gives you the probability of getting your values for A and B despite that A=B. If the probability is extremely low, you can say that there is high confidence that A is greater than B. Does that makes sense? https://en.wikipedia.org/wiki/P-value – Camilo Rada Apr 03 '19 at 23:49
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    In any case, I think this is a question for Cross Validated SE, not Earth Sciences, in spite of the data being related to Earth Sciences. – Camilo Rada Apr 04 '19 at 01:17
  • I read your post on Cross Validated, and there you ask for the uncertainty associated with the area under the curve, no the significance of a difference between areas. Those are very different question. The error is easy to calculate: if the error of each measurement is $\sigma_1, \sigma_2, \sigma_3, ..., \sigma_n$ and the time between samples is $\Delta t$, then the error in the area would be $\Delta t \sqrt{\sigma_2^2 + \sigma_3^2+...+\sigma_n^2}$ have a look at this http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm – Camilo Rada Apr 06 '19 at 15:34

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