I found this equation in a paper from D. Sornette and A. Johansen ('Large Financial Crashes', Physica A 245, pp. 411-422, 1997) and it is claimed that this equation describes a rising market before a crash.
With a market approaching the crash (or sharp correction), you can find the missing parameters in the equation via a fitting algorithmus, and the equation gives you the date of the crash and the future market behavior before the crash. Wouldn't that be nice for investing if it really works?
The theoretical background of the equation is the assumption that crowd behaviour can be modeled via complex system theory and above equation is related to such a model.
As you can see, there are 9 parameters in the equation to be found via fitting. If you remember mathematics, you can fit whatever you want with just enough parameters. In the paper they discuss why the equation still works, and they show that it worked well in various past markets.