The Long Memory of the Efficient Market

By Fabrizio Lillo, J. D. Farmer. 2003

387 citations recorded by the source corpus.

Abstract For the London Stock Exchange we demonstrate that the signs of orders obey a long-memory process. The autocorrelation function decays roughly as a power law with an exponent of 0.6, corresponding to a Hurst exponent H = 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 that act to make the returns whiter. We show that some institutions display long-range memory and others don’t.

Subfields: Economics and Econometrics, Finance

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Universal features of price formation in financial markets: perspectives from deep learning (2018, background): “There is a trove of empirical evidence going against this hypothesis, and pointing to long-range dependence in financial time series (Mandelbrot et al. 1997, Bouchaud et al. 2004, Lillo and Farmer 2004, Bacry et al. 2008, Taranto et al. 2014).”
The adaptive nature of liquidity taking in limit order books (2014, background): “This result confirms the results in [17], but now we can better understand what is happening in the order book.”
On Hurst exponent estimation under heavy-tailed distributions (2010, background): “In more detail, Hurst exponent of 0.5 indicates two possible processes – either an independent one (Beran, 1994) or a short-range dependent one (Lillo and Farmer, 2004).”
Some comments on Hurst exponent and the long memory processes on capital markets (2008, neutral): “[15] in London Stock Exchange.”
Relation between bid–ask spread, impact and volatility in order-driven markets (2006, background): “As a result there are in fact very strong high frequency correlations in the order flow, coming from the ‘hide and seek’ game played by buyers and sellers within the order book (Bouchaud et al. 2004, Lillo and Farmer 2004, Weber and Rosenow 2005).”
Anomalous price impact and the critical nature of liquidity in financial markets (2011, background): “However, we know from empirical data [3,21,26] that the signs of transactions t are in fact long-ranged correlated, i.”
Econophysics: Empirical facts and agent-based models (2009, neutral): “It has been observed in Lillo and Farmer (2004) for example that the autocorrelation function of the signs of trades (ǫn) was a slowly decaying function in n−α, with α ≈ 0.5.”
Limit theorems for nearly unstable Hawkes processes (2013, background): “Indeed, one of the most well documented stylized fact in high frequency finance is the persistence (or long memory) in flows and market activity measures, see for example [11, 35].”
Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics (2020, background): “But the most widespread indicator of market efficiency seems to be the Hurst exponent [51, 13, 56, 28].”
Beyond the Square Root: Evidence for Logarithmic Dependence of Market Impact on Size and Participation Rate (2014, neutral): “33 5.2 The fair pricing approach of Farmer et al. . . . . . . . . . . . . . . . . . . . . . . . 33 5.3 Other theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.4 A few caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6 ”
A Mathematical Approach to Order Book Modelling (2010, background): “in [3], and Lillo and Farmer in [13] (See also [9] and [2].”
The price impact of order book events: market orders, limit orders and cancellations (2009, background): “This is in contrast to several other papers (Bouchaud et al. 2004, 2006, 2009, Lillo and Farmer 2004), where the ’s are calculated for market orders only ( ¼MO0, MO0), and those signs are known to be strongly persistent among themselves, with, as recalled in section 2, a correlation decaying as a…”
Limit order books (2010, methodology): “The time series constructed by assigning the value +1 to incoming buy orders and −1 to incoming sell orders has been reported to exhibit long memory on the Paris Bourse (Bouchaud et al. 2004), the NYSE (Lillo and Farmer 2004) and the Shenzhen Stock Exchange (Gu and Zhou 2009a).”
Universal scaling and nonlinearity of aggregate price impact in financial markets. (2017, neutral): “[24] Fabrizio Lillo, J Doyne Farmer, et al.”