The Long Memory of the Efficient Market

Using data from 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 $H \approx 0.7$. The time $\tau$ is measured in terms of the number of intervening events. This is true for market orders, limit orders, and cancellations. Although the values for $\alpha$ vary from stock to stock, in the range 0.36 - 0.77, in most cases the exponents for different stocks are quite similar, and they are always less than one. 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 signs are compensated for by anti-correlated fluctuations in transaction size and liquidity. For example, when buy orders become more likely, buy orders tend to be smaller than sell orders and buy liquidity tends to be higher than sell liquidity. By breaking down the data by institutional codes we show that some institutions display long-range memory and others don't.