[Xcelerate]

> And then, the academic perspective is that prices should be modelled as random walks, though you may talk/learn about things such as "trend" and volatility.

The math involved in finance and economics always seems way behind that of other fields. The problem is that the other fields with more advanced math are so deep in theory that the people working in those areas are often either unaware of the potential real world applications of their work, or they are simply not interested in it (I’ve noticed there seems to be little overlap between the type of personality inclined to explore abstract theories as its own reward and the type of personality that prefers to apply existing knowledge to a real world problem).

> Suggesting that hidden variables/states/transitions can be learned from historical data is usually considered pseudo-scientific.

I mean, there’s a definitive answer to the question of stock market predictability. Unfortunately, it’s also uncomputable: if the conditional Kolmogorov complexity of a stock price time series given relevant auxiliary data is less than the size of the time series data (roughly speaking), then the stock price is predictable to some degree. Otherwise, it’s not.

I would be extremely skeptical if anyone claimed that stock price is truly Kolmogorov-random. However, I also think no single trading group’s algorithms (and data) are sufficiently more advanced than any other group’s to the point where algorithmic arbitrage is obvious to the market (or maintainable over a sufficiently long time period). I would not be surprised though if a sudden ML breakthrough destabilizes the entire market at some point in the near future when one group does in fact realize a step function improvement in their algorithms.