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A theory for long-memory in supply and demand


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  • F. Lillo
  • Szabolcs Mike
  • J. Doyne Farmer


Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power law distributed, this gives rise to power law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v to the power -alpha and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau to the power -(alpha - 1). This is a long-memory process when alpha

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Bibliographic Info

Paper provided by in its series Papers with number cond-mat/0412708.

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Date of creation: Dec 2004
Date of revision: Mar 2005
Handle: RePEc:arx:papers:cond-mat/0412708

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Cited by:
  1. Yamamoto, Ryuichi, 2011. "Order aggressiveness, pre-trade transparency, and long memory in an order-driven market," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1938-1963.
  2. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Papers physics/0603084,, revised Mar 2007.
  3. Bence Toth & Imon Palit & Fabrizio Lillo & J. Doyne Farmer, 2011. "Why is order flow so persistent?," Papers 1108.1632,
  4. Chiarella, C. & Iori, G. & Perello, J., 2008. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Working Papers 08/04, Department of Economics, City University London.
  5. Jonathan Donier, 2012. "Market Impact with Autocorrelated Order Flow under Perfect Competition," Papers 1212.4770,


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