  For the London Stock Exchange we demonstrate that the signs of orders obey a
long-memory process. The autocorrelation function decays roughly as
$\tau^{-\alpha}$ with $\alpha \approx 0.6$, corresponding to a Hurst exponent
$H \approx 0.7$. This implies that the signs of future orders are quite
predictable from the signs of past orders; all else being equal, this would
suggest a very strong market inefficiency. We demonstrate, however, that
fluctuations in order signs are compensated for by anti-correlated fluctuations
in transaction size and liquidity, which are also long-memory processes. This
tends to make the returns whiter. We show that some institutions display
long-range memory and others don't.
