Start by examining the periodogram of each time series to identify and compare any underlying periodic behavior. Finding the frequency where peak power occurs would be a good place to start. Another quick and dirty method would be to fit a sinusoidal function to your data to and examine the fitted parameter corresponding to the period. There are a number of different tools and techniques you can use here. I suggest playing around with a few to determine which best suits your needs.
Why not show the ime series properties of each data. Start my graph and do an augmented Dickey-Fuller (ADF) test on each level and times series. That is, easy and rigorous