Pseudorandom number generators and the stock market
As correlations are discovered in psuedorandom number generators used in simulations, the correlations are removed by creating better generators. So as time marches on, the state of the art PRNG's should be getting more and more random.
As correlations are discovered in the stock market, they are removed as the resevoir of correlation is drained for its profit. So the stock market should be getting more and more random as time goes on (especially as faster computers and more sophisticated statistical techniques are used)