[nnq]

besides karelp's sister comment, there's also the "obvious" fact that stock price is not a function of time, it's not P(t), it's a function of time and the entire f universe that also evolves through time, more like P(t, U(t, ....)) ....you can simplify things by assuming the laws of physics are deterministic and you only need one instance of the state of the universe, U, so you'd have P(t, U)

...now if you don't explicitly represent U as a parameter, you'll have it implicit in the function. So your "neural network" contains the entire state of the freakin universe (!!).

Ergo, contingent on your stance on theologic immanence vs. transcendence, what you'd call "neural network approximation of the stock's price function" is probably quite close to what other call... God (!).

(Now, if relativity as we know it is right, you might get aways with a "smaller slice of U" - lear about "light cone". And to phrase this in karelp's explanation context: you'd need to know U to know which of the practically infinitely many such neural networks to pick. The core of (artificial) intelligence is not neural networks in themselves, it's learning, the NN is a quite boring computational structure, but you can implement tractable learning strategies for it, both in code, and in living cells as evolution has shown...)

[DennisP]

And you'd have to know the state of U to infinite precision. Which makes me wonder whether neural nets have any hope with a simple chaotic function. Maybe they do but just in the short term, like predicting the weather.