It is known since Bachelier 1900 that price changes are nearly uncorrelated, leading to a random-walk like behaviour of prices. However, compared to the simplest Brownian motion, price statistics reveal a large number of anomalies, such as fat tails and long memory in the volatility.

The detailed study of trade by trade and order book data allows one to provide evidence for a subtle compensation mechanism that underlies the `random’ nature of price changes. This compensation drives the market close to a critical point, which may explain the sensitivity of financial markets to small perturbations, and their propensity to enter bubbles and crashes.

We argue that the resulting unpredictability of price changes is quite far from the neo-classical view that markets are informationally efficient.