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# The long memory of the efficient market

## Author

Listed:
• Fabrizio Lillo
• J. Doyne Farmer

## Abstract

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.

## Suggested Citation

• Fabrizio Lillo & J. Doyne Farmer, 2003. "The long memory of the efficient market," Papers cond-mat/0311053, arXiv.org, revised Jul 2004.
• Handle: RePEc:arx:papers:cond-mat/0311053
as

File URL: http://arxiv.org/pdf/cond-mat/0311053

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