The accuracy of GDP prediction, which - remember - amounts to the task of predicting everything there is without having "completed the science", is pretty decent all things considered.
Look for example at GDPnow forecast vs. reality. GDPnow is very spiky, since it changes constantly, but its performance is overall pretty accurate, and during each period its data use more than halves the RMSE. In other words, it has predictive power.
If you look at IMF predictions of world GDP [1] you can see that simply taking last year's value would have had lower error for most years and in average.
Look for example at GDPnow forecast vs. reality. GDPnow is very spiky, since it changes constantly, but its performance is overall pretty accurate, and during each period its data use more than halves the RMSE. In other words, it has predictive power.