Starting off with a linear regression is not unreasonable even if we suspect that the observations are not IID. I'm not completely sold on the existence of cycles, at least on a decadal scale. Purely random data can show lots of clumps suggestive of patters which are not really there. It would be very interesting to put the data through some sort of Fourier analysis to see if there any real periodicity, but I don't have the tools for that.