To prognosticate means to predict something or at least hint at what will happen in the future. When a lot of natural disasters start happening close together, you might prognosticate that the world is ending, a prediction that's actually thousands of years old.
From the Latin prognosticāre, meaning "make a prediction," the verb prognosticate means to foretell or predict what is coming. While a fortuneteller or palm reader might claim special powers for seeing into the future, you can prognosticate by looking at real evidence and making a reasonable conclusion about how events will unfold. Sometimes, though, what you prognosticate from a dream or a fortune-cookie message ends up happening too, which is less reasonable but pretty neat — unless the world really does end.