I have a 2 dimensional geographic space. There are crime events occuring at different regions in the space over time. I am looking particularly at property crimes like burglary. If I look at the time series of burglary events over the entire 2-d space, I can see an obvious periodicity based upon the frequency spectrum of the Fourier Transform.
I believe that different parts of the space exhibit different periodicities, i.e., different frequency spectrums.
So I have events per location indexed by date and time. So I can say a burglary happened on Wed May 3, 2017 at 12:00noon on the block of Venice blvd and Robertson in Los Angeles. I have tens of thousands of events indexed this way, with data from 2010 till present. You are correct that there is a seasonal trend and also a weekly trend, and a daily trend. However there tend to be differences in two ways. First, there is some variation in the number of events in a day--so the height of the frequency. There might also be the introduction of some new frequencies--though small--in intermittent ranges between the normal daily, weekly, and seasonal trends. These new frequencies are relatively hard to detect unless I have a good window on the period.
My goal was to find a way to detect the boundaries of regions in which the spectrum seems equivalent, so that I can thereby identify the regions of distinct periodicities.
I have been looking at material on change point detection and and such, but have not found any articles relating to my question. I just might be looking under the wrong names or something.
In looking at the Signal Processing literature, seems like I need to do a sliding window. But I am not sure how to detect the change point in the frequency spectrum as the window grows in size.
Once I have the change detection locked down, then I can basically just growth the sliding window by randomly starting at different points in the space. If I ran the simulation hundreds of times, I could try and find the regions where 90% of the simulations overlap, etc.
Does anyone know of a technique to detect the change points that I am trying to detect?