Linear regression & correlation for time series data

#1
Hi all,

I've searched wide and can only find warnings about NOT applying common linear regression and correlation statistics to time series data, as that may violate the independence requirement. However, I haven't found what methods should be used instead?

I would like to determine if my data have a (linear) trend significantly different from 0 (as a normal correlation would provide), and what the rate (slope) is. My data set consists of 5 years (5 annual sample times) of soil carbon data from reforestation plots. (FYI - many terrestrial afforestation projects show a decrease in the first 5 years. I expect mangrove forests should increase from year 0.)

Thanks for your consideration.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
You could probably add more details in regards to your data. As of now it is unclear is you have multiple groups that you may compare or not.

There is probably a better option, but an Armitage-Cochran Trend Test may work. You may want to read more about it to see if it may be the best option for you.
 
#3
Yes, I have two groups (tree species). I wasn't considering this in my thought to use linear regression and correlation though. l was planning to analyze each group separately, simply using time as the independent variable and soil carbon content as the dependent variable, to determine if either forest type showed a positive trend in soil carbon over time.

But to answer clearly your request for more details:
Species: 2
Sample time points: 5 (at not exactly regular sampling intervals)
Soil carbon: (measurement variable) (3 measurements at each time point, so a total of 15 samples per species)

I was considering using ANCOVA (as discussed in another post) to assess any difference in the rate of soil carbon change between the two forest types. This is a secondary question in my research.

I looked into the Armitage-Cochran Trend Test, and not sure it's appropriate. It seems the most common application is for proportions (and like I said, I was planning to test each forest type separately, but maybe that is a problem?). Also, SPSS apparently can't do this test. Is there a more standard test to consider for this dat set?

Please forgive my ignorance on this issue, and thank you much for your thoughts. It's been many years since I've worked with statistics, so I'm struggling to get my mind around the concepts again.