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# The long memory of the efficient market

## Author Info

• 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.

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

Paper provided by arXiv.org in its series Papers with number cond-mat/0311053.

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Date of creation: Nov 2003
Date of revision: Jul 2004
Handle: RePEc:arx:papers:cond-mat/0311053

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Web page: http://arxiv.org/

## Related research

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• C00 - Mathematical and Quantitative Methods - - General - - - General
• C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
• G00 - Financial Economics - - General - - - General
• G1 - Financial Economics - - General Financial Markets

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