I am interested in looking for periodicities in a several day long recording of electrical activity. The traces present a very steady baseline over which, from time to time, some short events (300-500 ms) appear (hence the sparse in the title, although I am not sure it is the right term to use).
Now, the nature of the data prevents me to analyse the trace as a whole (~20 days recorded at 10KHz, my computer will definitely not handle that), so I just wrote a series of routines to find the interesting events, and export their date/time (also their shape, but that is another story) to a text file.
So, I end up with a series of times to analyse.
Just by looking at the raw trace what I can see is:
- A ~2 hours periodicity in the events
- The events appear in groups. That is, I have a series of 20-30 events in the course of a couple of minutes, then nothing for ~2 hours, then other 20-30 events and so on. Note that the number of events in a group is variable, can be 30 in one and 5 in the next one.
- The periodicity is fairly obvious, but it's not perfect: events happen roughly at 2 hours interval, and the exact time may vary from day to day.
- There may be superimposed periodicities. In particular, I see events at a specific time of the day, which may or may not fit in the abovementioned 2 hours periodicity.
What can I do to statistically determine the periodicity?
What I have tried to do is to make a frequency histogram of the events, binning every 10 minutes, which empirically seemed like a sensible bin size, and then looking at the ACF or the FFT of the counts, but only in a few cases something pops out with the ACF (nothing with FFT).
So, how would you analyse this type of problem?
Bonus question: in certain cases I have missing data (1 or 2 days missing for technical reasons). How would I account for that?
PS: I am using R, but any non-R solution will do as well!
Here is some sample data to play with: http://dl.dropbox.com/u/11676289/exampletimes.txt
Here is a plot of the times:
and their histogram, in 10 minutes breaks