Existence of various "cycles" in the stock market is a rather questionable topic. However, it is easy to measure business cycles (recessions etc) and stock market and economy are of course closely related. Data about business cycles can be found in the attached link. Business cycle literature is very extensive, you will find it easily.
You need to research the NBER works on this matter. I know that they research cycles for real GDP, real income, employment, industrial production, and wholesale-retail sales. I attach a recent download of their cyclical analysis for a historical period.