Finding periodicity in discrete events I have a program that detects events in a large amount of measurement data. When it detects an event, it writes a timestamp. I have thousands of event timestamps. What I wish to do is detect if there is periodicity in the timestamps I have. 

Pictures may aid my explanation: If I have a bunch of events on a timeline, as in the figure below, the events all seem to be random but there may be some kind of periodic component to the events.



What I wish to do is detect if any of the seemingly random events are following a strict repeating interval. An illustration is given below, where we see that in the seemingly random events above there are some data points that are repeating with a fixed frequency. 



I am not certain what kind of method to apply. I have looked into power spectral density, fourier transform and ARIMA. I applied fourier transform (as in the answer here) but was not able to make anything meaningful out of it.  

Properties of the applied method should possibly include: 


A quantitative measure of how strict or fixed the intervals are, or how 
certain we can be that we have detected a fixed cycle
The ability to detect periodicity on different timescales (e.g. events occurring multiple times within the same hour or multiple times during a week with a fixed pattern)


Anyone has suggestions how this could be done?
See "ePeriodicity: Mining Event Periodicity from Incomplete Observations" by Zhenhui Li, Jingjing Wang, and Jiawei Han (2013); preprint at https://faculty.ist.psu.edu/jessieli/Publications/tkde14.pdf