<p>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.</p>

CC BY-SA 4.0
2019-04-03T17:09:59.260Z
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
CC BY-SA 4.0
2019-04-03T17:45:17.230Z
Yes, I mean testing the statistical significance of the difference
y chung
CC BY-SA 4.0
2019-04-03T18:12:50.100Z
Do you know the error associated with each data point?
Camilo Rada
CC BY-SA 4.0
2019-04-03T20:12:00.833Z
Yes, I have standard error of each GHG flux data point
y chung
CC BY-SA 4.0
2019-04-03T23:49:29.597Z
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
CC BY-SA 4.0
2019-04-04T01:17:14.527Z
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
CC BY-SA 4.0
2019-04-06T15:34:08.650Z
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
<greenhouse-gases>
Testing the statistical significance of the difference between cumulative/integrated emission quantities calculated from time series?
y chung
# Testing the statistical significance of the difference between cumulative/integrated emission quantities calculated from time series?

(Asked by: username_0 on 2019-04-03)

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.

**Tags:** greenhouse-gases

> **Comments:**
> **username_1**: 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.  
> **username_0**: Yes, I mean testing the statistical significance of the difference  
> **username_1**: Do you know the error associated with each data point?  
> **username_0**: Yes, I have standard error of each GHG flux data point  
> **username_1**: 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  
> **username_1**: 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.  
> **username_1**: 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  

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## 0 answers

