It's a tough call to come up with 'original thought' in a thread comment. But I can give some pointers about non-linear methods that work.

Time delay embedding is a common method to estimate hidden structure in the system. You can make short-term predictions about future state of the system if you look at its previous states and find ones that are similar to current one. You can analyse transitional probabilities between these states. You can also study scale-invariant properties of the system such as fractal dimension or log-time scaling. There is a separate discipline called 'chaos control' that looks at certain unstable moments when the system can be manipulated by a small external signal (very relevant for dealing with heart attacks, should be interesting for central banks as well).

So, most categorically, current mainstream economic models are by far not the best we can do with at the time. They are grossly inaccurate representation of reality. There is of course emerging field of 'complexity economics' but it is not even close to being accepted in the mainstream.