nad,
The tidal experiment is very simple and a spreadsheet is all you need. Take the tidal gauge data, filter on a 12-month box window, and subtract the current value from a value referenced from 2 years ago. Repeat that backwards for all previous points. Then overlay with the SOI data.

Do you think the 3-month shift is significant? That simply gave the optimal fit -- a fit using the current month may be nearly as good.