I have several groups of stochastic data that I would like to analyze.
I would like to rank each group of data according to how symmetric it is about the x axis. In other words, if I have a sine wave, its symmetry would be 100%
I was thinking about applying a fourier transform to the data to put it into the frequency domain and then make a periodogram out of it. With this, I can see what frequency prevails over others in each group of data.
However, with this approach, I cannot really estimate how periodic the data is without looking at it. With the above sine wave example, if one were to take a look at it, it would be fairly easy to recognize that it is oscillating at one frequency, but for more stochastic data, it would be much harder. So, what I want to do is compare the most common frequency with all the others so that I can come up with some sort of metric to measure its symmetry. Does anybody have any ideas?