This is of the S&P 500 from Yahoo. The lower line starts on Feb 1, 2006, and the two peaks are Apr 30, 2007 and Sept 30 2007, and the lower black dot is Jan 1 2008.
The upper line starts about Apr 30 2014, and the last peak before the dip was June 30 2015, with the dip on Aug 31 2015, and the peak after the dip on Sep 30 2015. The upper black dot is Jan 1 2016.
I would say, visually, that the two periods appear to roughly coordinate since Sept 30 2007 and Sept 20 2015.
Another link seeing an 8 year cycle. It might be interesting to post news from 8 years ago.
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