Chaos theory does provide us with a tool here: The Lyapunov exponent[1] and the related Lyapunov time[2]. These allow you to characterize how far into the future you can expect to be able to predict the behavior of a dynamical system. To Prerok’s example of predicting the weather, this is why 3 day weather forecasts tend to be great, 10 day weather forecasts tend to be good, and weather forecasts two months out are just the general average trends for the climate in that time and place.
There are chemical systems where Lyapunov time is small enough that you can only predict seconds or minutes into the future and astronomical systems that are nonlinear and chaotic but have a long enough Lyapunov time that you can make reasonable predictions for millions of years. For both of these scales, the Lyapunov time still bounds how far into the future you can expect your predictions to remain near to the actual behavior of the system.
I do not know the Lyapunov times of the financial markets. That said, mathematically-sophisticated professional analysis frequently get their predictions wrong in major ways, so I expect there is a pretty hard bound on predictive quality caused by a short Lyanpunov time of the markets themselves.