Order book model with herd behavior exhibiting long-range memory

Kononovičius, Aleksejus; Ruseckas, Julius

doi:10.1016/j.physa.2019.03.059

Cited by 16 publications

(16 citation statements)

References 69 publications

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“…Agent-based binary-state models are commonly used to study the effect that simple individual dynamical rules may have on the collective behavior of a system. Typical examples include modeling the spreading of diseases [1,2], the time evolution of the number of speakers of a determined language [3][4][5][6], the evolution of prices in financial markets [7][8][9][10][11][12][13], or the dynamics of opinion formation in a population of individuals [14][15][16]. As a prominent case of the latter, the voter model [17][18][19] and its variants thereof [20], by which an agent adopts with some probability the state of a randomly chosen neighbor, are widely used when the mechanism at hand is that of imitation.…”

Section: Introductionmentioning

confidence: 99%

Ordering dynamics in the voter model with aging

Peralta

Khalil

Toral

2020

Physica A: Statistical Mechanics and its Applications

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The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The "internal age", or time an individual spends holding the same state, is added to the set of binary states of the population, such that the probability of changing state (or activation probability pi) depends on this age. A closed set of integro-differential equations describing the time evolution of the fraction of individuals with a given state and age is derived, and from it analytical results are obtained characterizing the behavior of the system close to the absorbing states. In general, different age-dependent activation probabilities have different effects on the dynamics. When the activation probability pi is an increasing function of the age i, the system reaches a steady state with coexistence of opinions. In the case of aging, with pi being a decreasing function, either the system reaches consensus or it gets trapped in a frozen state, depending on the value of p∞ (zero or not) and the velocity of pi approaching p∞. Moreover, when the system reaches consensus, the time ordering of the system can be exponential (p∞ > 0) or power-law like (p∞ = 0). Exact conditions for having one or another behavior, together with the equations and explicit expressions for the exponents, are provided.

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Section: Introductionmentioning

confidence: 99%

Ordering dynamics in the voter model with aging

Peralta

Khalil

Toral

2020

Physica A: Statistical Mechanics and its Applications

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“…In [ 119 , 120 ], we have explored the opportunities to control the fluctuations in the artificial financial markets driven by the herding ABM, showing that the random trading, control strategy suggested in [ 121 ], may also destabilize the market. In [ 42 ], we have removed the assumption about the exogenous noise and replaced it with order book dynamics, thus presenting another possible explanation for fracture in the PSD: it also arises due to market price lagging behind the changes in the equilibrium price, Equation ( 54 ). Notably, the order book version of the model was able to reproduce both trading activity and absolute return statistical properties at the same time.…”

Section: Agent-based Model Of the Long-range Memory In The Financial Marketsmentioning

confidence: 99%

“…ABM) [ 39 , 40 ], too. With time, we have developed more complicated ABMs to account for the separation of time scales and order flow [ 41 , 42 ]. We have even branched out into sociophysics [ 43 , 44 , 45 , 46 ] as we have understood that the herding ABM we used to model the financial market is essentially equivalent to the well-known voter model [ 47 , 48 , 49 ].…”

Section: Introductionmentioning

confidence: 99%

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Kazakevičius

Kononovičius

Kaulakys

et al. 2021

Entropy

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In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

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“…In this section we use Eq. (7) to fit bursting statistics obtained from the order book model exhibiting longrange memory [47]. From this model we have obtained numerical absolute return time series.…”

Section: Bursting Statistics Of the Order Book Model Exhibiting Long-mentioning

confidence: 99%

“…(7), is rather good. The parameters of the fits were obtained by matching four empirical moments (mean, variance, [47]. Threshold level was set at 3 standard deviations of the numerical time series.…”

Section: Bursting Statistics Of the Order Book Model Exhibiting Long-mentioning

confidence: 99%

Approximation of the first passage time distribution for the birth–death processes

Kononovičius¹,

Gontis²

2019

J. Stat. Mech.

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We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death processes and the sophisticated order-book model exhibiting long-range memory. We discuss how our approach contributes to the competition between spurious and true long-range memory models.

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Order book model with herd behavior exhibiting long-range memory

Cited by 16 publications

References 69 publications

Ordering dynamics in the voter model with aging

Ordering dynamics in the voter model with aging

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Approximation of the first passage time distribution for the birth–death processes

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