If you use Google Trends (a tool to illustrate the frequency of search terms) and search for the word "war" with USA as geographic region, you will be presented with the graph below showing monthly data from 2004 - 2019 (I have added the dates for emphasis);
The trend appears to be very periodic, on the same scale as "job," which economists will often say is closely related to the annual economic cycle of employment. As can be seen in the graph below;
However, if you search for the word "peace," there is no such periodicity;
If you change the region to another English speaking country such as the United Kingdom, the periodicity of "war" is still somewhat present but less pronounced, appears to be decaying and is instead shifted to peak around September - November.
What would be an efficient way, from a statistical point of view, to determine what is the cause to the periodicity of "war" in the region of USA?
Since correlation does not imply causation, I don't know how to effectively tackle this problem mathematically. Any ideas/approaches would be much appreciated!
In economics/econometrics there are some approaches to establish causality, but all of these approaches require you to have an idea/hypothesis about what a potential cause is (and to get data on them). It seems to me you are not there yet, so that's the first step: Get some ideas of potential causes.
Then, correlation does not imply causation, but causation does imply correlation. So in a first test you could check your potential causes against the data. Say there is a TV series in the US with the name "war" in it. Check the broadcasting dates and compare them to the spikes in the google trend data. If there is a correlation you passed the first test. To really nail a causal relationship you will have to do more, of course, but this might get you pretty far. If there is no correlation then the candidate is not the cause.
To efficiently do this step, you could export the google trends data and get time series for all of the potential causes. Then run a time series multiple regression, or some Granger causality tests, to help you quickly determine which among the potential causes have explanatory power (i.e., are correlated). Again, while this does not necessarily establish causation, it helps you rule out many potentials and narrow down the list.