step 1: get a noisy time series
step 2: filter out everything that doesn't come in 9 year cycles
the exchange rate between the US Dollar and UK Pound
UK/US exchange rate 1791-2007 less 9 yr. mov.avg
result: you got something with a 9 year cycle, didn't you?
an 8.25 year cycle
Just the same way wind instruments work. Make white noise, and pass it through a tube of a certain length, an it filters out all the frequencies that don't resonate, leaving just the frequency you want and some of its harmonics.