  We investigate the random walk of prices by developing a simple model
relating the properties of the signs and absolute values of individual price
changes to the diffusion rate (volatility) of prices at longer time scales. We
show that this benchmark model is unable to reproduce the diffusion properties
of real prices. Specifically, we find that for one hour intervals this model
consistently over-predicts the volatility of real price series by about 70%,
and that this effect becomes stronger as the length of the intervals increases.
By selectively shuffling some components of the data while preserving others we
are able to show that this discrepancy is caused by a subtle but long-range
non-contemporaneous correlation between the signs and sizes of individual
returns. We conjecture that this is related to the long-memory of transaction
signs and the need to enforce market efficiency.
