A Theory for Long-Memory in Supply and Demand

Lillo, Fabrizio; Mike, Szabolcs; Farmer, J. Doyne

doi:10.2139/ssrn.708303

Cited by 41 publications

(72 citation statements)

References 26 publications

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“…We also find long-memory on signed order flow as demonstrated in Lillo, Mike, and Farmer (2005). We again divide the sample per pseudo-clock time, and denote the period as +1 (-1) when the majority of orders are buyer (seller) initiated in a period.…”

Section: Market Orders and Efficient Marketmentioning

confidence: 80%

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Long-memory in an order-driven market

LeBaron

Yamamoto

2007

Physica A: Statistical Mechanics and its Applications

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This paper introduces an order-driven market with heterogeneous investors, who submit limit or market orders according to their own trading rules. The trading rules are repeatedly updated via simple learning and adaptation of the investors. We analyze markets with and without learning and adaptation. The simulation results show that our model with learning and adaptation successfully replicates long-memories in trading volume, stock return volatility, and signs of market orders. We also discuss why evolutionary dynamics are important in generating these long memory features.2

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Section: Market Orders and Efficient Marketmentioning

confidence: 80%

“…Finally, the signs of market orders follow a long-memory process (Lillo, Mike, and Farmer (2005)); yet the market is efficient ).…”

Section: Introductionmentioning

confidence: 99%

Long-memory in an order-driven market

LeBaron

Yamamoto

2007

Physica A: Statistical Mechanics and its Applications

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“…autocorrelated and highly persistent 9 , and pointed out that they can be caused either by order splitting or herding. Lillo, Mike and Farmer (2005) introduced a model for order splitting connecting the size of large orders with the autocorrelation of order flow and showed that its predictions gave good agreement with data from the London Stock Exchange. Gerig (2007), demonstrated that for the LSE stock AZN the trades coming from the same brokerage have long-memory, whereas trades from different brokerages do not (see also Bouchaud, Farmer, and Lillo (2009)).…”

Section: Introductionmentioning

confidence: 98%

Why is equity order flow so persistent?

Tóth

Palit²,

Lillo

et al. 2015

Journal of Economic Dynamics and Control

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Order flow in equity markets is remarkably persistent in the sense that order signs (to buy or sell) are positively autocorrelated out to time lags of tens of thousands of orders, corresponding to many days. Two possible explanations are herding, corresponding to positive correlation in the behavior of different investors, or order splitting, corresponding to positive autocorrelation in the behavior of single investors. We investigate this using order flow data from the London Stock Exchange for which we have membership identifiers. By formulating models for herding and order splitting, as well as models for brokerage choice, we are able to overcome the distortion introduced by brokerage. On timescales of less than a few hours the persistence of order flow is overwhelmingly due to splitting rather than herding. We also study the properties of brokerage order flow and show that it is remarkably consistent both cross-sectionally and longitudinally.

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“…A cogent one, which was proposed by Lillo et al [9], is that investors tend to strategically split their large hidden orders into small pieces before execution to prevent the increase in the trading costs. Empirical findings partially support this explanation.…”

Section: Introductionmentioning

confidence: 99%

Signs of Market Orders and Human Dynamics

Murai

2015

Proceedings of the International Conference on Social Modeling and Simulation, Plus Econophysics Colloquium 2014

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A time series of signs of market orders was found to exhibit long memory. There are several proposed explanations for the origin of this phenomenon. A cogent one is that investors tend to strategically split their large hidden orders into small pieces before execution to prevent the increase in the trading costs. Several mathematical models have been proposed under this explanation.In this paper, taking the bursty nature of the human activity patterns into account, we present a new mathematical model of order signs that have a long memory property. In addition, the power law exponent of distribution of a time interval between order executions is supposed to depend on the size of hidden order. More precisely, we introduce a discrete time stochastic process for polymer model, and show it's scaled process converges to a superposition of a Brownian motion and countably infinite number of fractional Brownian motions with Hurst exponents greater than one-half. IntroductionEmpirical studies [2,6,8,11] on high frequency financial data of stock markets that employ the continuous double auction method have revealed a time series of signs of market orders has long memory property. In contrast, a time series of stock returns is known to have short memory property. A time series of order signs is defined by changing transactions at the best ask price into C1 and transactions at the best bid price into 1. The auto-correlation function of the order signs decays as a power law of the lag and the exponent of the decay is less than 1, which is equivalent to a Hurst exponent of the time series is greater than one-half.In this paper, we propose a new mathematical model which takes account of origin of the long memory in order signs. As a first step, we define a discrete time stochastic process of cumulative order signs in accordance with some explanation

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A Theory for Long-Memory in Supply and Demand

Cited by 41 publications

References 26 publications

Long-memory in an order-driven market

Long-memory in an order-driven market

Why is equity order flow so persistent?

Signs of Market Orders and Human Dynamics

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