Finding if data in array is periodic
Mathematically, what you probably want is the autocorrelation function. That function is a function on a function over time or a sequence, which gives you info about how similar your signal is to itself when shifted by shift $\tau$. 

If your signal is periodic with period $\tau$, then it will be very similar to itself when shifted by $\tau$, $2\tau$, $3\tau$, and so on. So, you'll get $\tau$-periodic peaks in your autocorrelation function

A very common thing to do is to look at the Power Spectral Density (PSD), which is, in fact, the Fourier transform of the autocorrelation function. You can, however, in your sampled case, calculate the PSD directly by Fourier-transforming (Matlab function fft) your sequence and finding the abs² of it. The peaks correspond to periodicities.