# Compare how fast two time-series grow

I collected data from Pubmed containing articles published about two different topics.

The first is a yearly series of articles about omega 3 supplements. The second is a yearly series of articles published about probiotics supplements.

I want to understand how fast the research has grown over time (in plain English, capture the scientific interest over time) and specifically whether the scientific interest grew somehow "faster" for a topic rather than the other.

Please find here the data in a public gdoc:

I don't expect a full solution but at least some indication to where to start looking for my answer.

I assume it is something I can check with the time series slope, but I need some more inputs for going deeper in my research because I am kind of lost. Thank you!

• Your linked data shows a large jump in the value of "probiotics" from 1970 to 1974, changing from 59 to 475, but I do not see this on your plot of the data. Both "omega" and "probiotics" show a sudden drop from year 2018 to year 2019 but again I do not see this on your plots. Would you please chech that the posted data link and plots match in this? – James Phillips Jul 31 '19 at 17:49

This is very similar to looking at stock prices and other financial variables in econometric analysis. The way to do this would be to plot $$\log(x_{t+1}) - \log(x_t)$$ at each time period $$t = 1,...,T-1$$. This will show the rate of growth of each of the series, which is a good measure of "how fast they are growing". (Note that if you have any zero values in your data then the growth to the next non-zero value is infinite.)