I am generally leery of cycle theories that involve fixed intervals of years. Many of them are rooted in astrology and planetary cycles which I do not believe influence world events. However, it is possible that some of these time intervals could coincidentally be pertinent to the stock market for socioeconomic reasons.
One time-interval that does seem to have significance is a 28-year interval from one important high to another, and from one important low to another, first discovered by George Lindsay, a famous market technician of the previous century.
The 28-year cycle is significant now because 2015 is 28 years from 1987, in which there was a 2-month crash during Aug-Oct that dropped the Dow 41%. Thus, 1987 had both an important high and low, so the 28-year cycle suggests an important top, bottom, or both during 2015-2016.
Here are some previous instances that I have identified (give or take a year). All of the lows came after drops of at least 17%, with many being 20-30%.
Lows of 1982 & 2010 (or 2011)
Highs of 1980 & 2007
Lows of 1974 & 2002
Highs of 1973 & 2000
Lows of 1970 & 1998
Lows of 1962 & 1990
Highs of 1959-60 & 1987
Corrections of 1956-57 & 1983-84
Lows of 1946 & 1974
Lows of 1942 & 1970
Lows of 1938 & 1966
Lows of 1932 & 1960
Lows of 1921 & 1949
See my previous posts for more information on 2015.