# Aleksejus KononoviciusVilnius University · Institute of Theoretical Physics and Astronomy

Aleksejus Kononovicius

PhD

## About

57

Publications

8,725

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597

Citations

Introduction

Senior researcher at Institute of Theoretical Physics and Astronomy (Faculty of Physics, Vilnius University). Research interests: stochastic and agent-based modeling, complex systems, Econophysics, Sociophysics, Statistical Physics and Data Science. Contributor to Physics of Risk science blog.

Additional affiliations

September 2016 - August 2021

Education

October 2011 - December 2015

## Publications

Publications (57)

In this contribution we analyze vote share distribution across the polling stations during Lithuanian parliamentary elections of 1992, 2008 and 2012. We find that the vote share distributions are rather well fitted by the Beta distributions. To reproduce this empirical observation we propose a multi-state agent-based model in which all agents choos...

Numerous models in opinion dynamics focus on the temporal dynamics within a single electoral unit (e.g. country). The empirical observations, on the other hand, are often made across multiple electoral units (e.g. polling stations) at a single point in time (e.g. elections). Aggregates of these observations, while quite useful in many applications,...

Latane social impact theory predicts recruitment and supportive interactions being responsible for opinion formation. So far only recruitment interactions were considered in the voter models. Here we consider a noisy voter model with supportive interactions, which make voters less likely to change their opinions. This is similar to the voter models...

We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We...

We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous two-agent interactions. In our analysis, we require that the polling period aligns with the delay in announcing poll o...

We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous two-agent interactions. In our analysis, we require that the polling period aligns with the delay in announcing poll o...

Demographic heterogeneity is often studied through the geographical lens. Therefore it is considered at a predetermined spatial resolution, which is a suitable choice to understand scalefull phenomena. Spatial autocorrelation indices are well established for this purpose. Yet complex systems are often scale-free, and thus studying the scaling behav...

Previously we have shown that pure 1/f noise arises from the trapping-detrapping process when traps are heterogeneous. Namely, the trapping-detrapping process relies on the assumption that detrapping rates of individual trapping centers in the condensed matter are random and uniformly distributed. Another assumption underlying the trapping-detrappi...

We propose a model of 1/f noise in semiconductors based on the drift of individual charge carriers and their interaction with the trapping centers. We assume that the trapping centers are homogeneously distributed in the material. The trapping centers are assumed to be heterogeneous and have unique detrapping rates. We show that uniform detrapping...

We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure 1/f noise can be observed until ex...

We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We...

We analyze the power spectral density of a signal composed of non-overlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of non-overlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure $1/f$ noise can be observed unti...

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non-Markovian point process exhibit power-law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a po...

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non-Markovian point process exhibit power-law scaling. We show that a nonlinear Markovian point process can reproduce the same scaling behavior. This result indicates a po...

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 proce...

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 proce...

Voter models are well known in the interdisciplinary community, yet they have not been studied from the perspective of anomalous diffusion. In this paper, we show that the original voter model exhibits a ballistic regime. Nonlinear transformations of the observation variable and time scale allow us to observe other regimes of anomalous diffusion as...

Voter models are well known in the interdisciplinary community, yet they haven't been studied from the perspective of anomalous diffusion. In this paper we show that the original voter model exhibits ballistic regime. Non-linear transformations of the observation variable and time scale allows us to observe other regimes of anomalous diffusion as w...

We examine parliamentary presence data of the 2008-2012 and the 2012-2016 legislatures of Lithuanian parliament. We consider cumulative presence series of each individual representative in the data set. These series exhibit superdiffusive behavior. We propose a modified noisy voter model as a model for the parliamentary presence. We provide detaile...

We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for th...

We consider a previously unexplored noisy voter model with supportive interactions. The agents in this model encourage other agents in the same state to keep their current state. We examine two different ways in which the support could be implemented: support deterring imitation as well as independence, support deterring imitation only. Both assump...

We examine parliamentary presence data of the 2008-2012 and the 2012-2016 legislatures of Lithuanian parliament. We consider cumulative presence series of each individual representative in the data set. These series exhibit superdiffusive behavior. We propose a modified noisy voter model as a model for the parliamentary presence. We provide detaile...

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 sophisticate...

In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and financial herd behavior model. Combining these approaches allows us to propose a model that replicates the long-r...

The coefficient of determination, known as R2, is commonly used as a goodness-of-fit criterion for fitting linear models. R2 is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to a dat...

Numerous models in opinion dynamics focus on the temporal dynamics within a single spatial unit (e.g., country). While the opinions are often observed across multiple spatial units (e.g., polling stations) at a single point in time (e.g., elections). Aggregates of these observations, while quite useful in many applications, neglect the underlying s...

We do consider models of the population or opinion dynamics which result in non-linear stochastic differential equations (SDEs) exhibiting spurious long-range memory. In this context, the correspondence between the description of birth-death processes as continuous-time Markov chains and continuous SDEs is of high importance for the alternatives of...

Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P.Ferreira [Physica A 500: 92-96] detrended fluctuation analysis was applied to the NBA teams' win records. It was shown that 28 considered NBA teams exhibit persistence in...

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 sophisticate...

Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P.Ferreira [Physica A 500: 92-96] detrended fluctuation analysis was applied to the NBA teams' win records. It was shown that 28 considered NBA teams exhibit persistence in...

Among the sports fans beliefs about "hot hands" and "winning streaks" are widely spread, while the scientific debate about these effects is still ongoing. Recently in a paper by P.Ferreira [Physica A 500: 92-96] detrended fluctuation analysis was applied to the NBA teams' win records. It was shown that 28 considered NBA teams exhibit persistence in...

The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to...

In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] as well as financial herd behavior model. Combining these approaches allows us to create a more plausible financial m...

It is widely accepted that there is strong persistence in financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equat...

Competition between varying ideas, people and institutions fuels the dynamics of socio-economic systems. Numerous analyses of the empirical data extracted from different financial markets have established a consistent set of stylized facts describing statistical signatures of the competition in the financial markets. Having an established and consi...

The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example of Markov processes with spurious memory is stochastic process driven by a non-linear stochastic differential...

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading ac...

We investigate the volatility return intervals in the NYSE and FOREX markets.
We explain previous empirical findings using a model based on the interacting
agent hypothesis instead of the widely-used efficient market hypothesis. We
derive macroscopic equations based on the microscopic herding interactions of
agents and find that they are able to re...

The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the thermodynamic limit the extensivity of the Tsallis entropy with as well as a q-Gaussian distribution. The dynam...

A characteristic feature of complex systems in general is a tight coupling between their constituent parts. In complex socio-economic systems this kind of behavior leads to self-organization, which may be both desirable (e.g. social cooperation) and undesirable (e.g. mass panic, financial “bubbles” or “crashes”). Abundance of the empirical data as...

Auto-regressive conditionally heteroskedastic (ARCH) family models are still
used, by practitioners in business and economic policy making, as a conditional
volatility forecasting models. Furthermore ARCH models still are attracting an
interest of the researchers. In this contribution we consider the well known
GARCH(1,1) process and its nonlinear...

A characteristic feature of complex systems in general is a tight coupling
between their constituent parts. In complex socio-economic systems this kind of
behavior leads to self-organization, which may be both desirable (e.g. social
cooperation) and undesirable (e.g. mass panic, financial "bubbles" or
"crashes"). Abundance of the empirical data as...

Systems with long-range interactions often exhibit power-law distributions
and can by described by the non-extensive statistical mechanics framework
proposed by Tsallis. In this contribution we consider a simple model
reproducing continuous transition from the extensive to the non-extensive
statistics. The considered model is composed of agents int...

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous em...

Collective behavior of the complex socio-economic systems is heavily
influenced by the herding, group, behavior of individuals. The importance of
the herding behavior may enable the control of the collective behavior of the
individuals. In this contribution we consider a simple agent-based herding
model modified to include agents with controlled st...

Purpose – The focus of this contribution is the correspondence between collective behavior and inter-individual interactions in the complex socio-economic systems. Currently there is a wide selection of papers proposing various models for the both collective behavior and inter-individual interactions in the complex socio-economic systems. Yet the p...

We derive a system of stochastic differential equations simulating the
dynamics of the three agent groups with herding interaction. Proposed approach
can be valuable in the modeling of the complex socio-economic systems with
similar composition of the agents. We demonstrate how the sophisticated
statistical features of the absolute return in the fi...

We propose a Markov jump process with the three-state herding interaction. We
see our approach as an agent-based model for the financial markets. Under
certain assumptions this agent-based model can be related to the stochastic
description exhibiting sophisticated statistical features. Along with power-law
probability density function of the absolu...

We present examples of agent-based and stochastic models of competition and
business processes in economics and finance. We start from as simple as
possible models, which have microscopic, agent-based, versions and macroscopic
treatment in behavior. Microscopic and macroscopic versions of herding model
proposed by Kirman and Bass diffusion of new p...

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the nonlinear stochastic models of long-range memory in financial markets. The agent based mode...

We investigate large changes, bursts, of the continuous stochastic signals,
when the exponent of multiplicativity is higher than one. Earlier we have
proposed a general nonlinear stochastic model which can be transformed into
Bessel process with known first hitting (first passage) time statistics. Using
these results we derive PDF of burst duration...

Many complex systems exhibit quiet periods separated by events of rapid evolution. Such systems often produce noise with the power-law characteristics, which can be modeled in terms of avalanches. The universal nature of the power-law behavior suggests that it does not arise as a consequence of particular interaction but it is a characteristic sign...

Simulation serves as a third way of doing science, in contrast to both
induction and deduction. The web based modeling may considerably facilitate the
execution of simulations by other people. We present examples of agent-based
and stochastic models of competition and business processes in economics. We
start from as simple as possible models, whic...

In the last sections we introduced a double stochastic process driven by the nonlinear scaled SDE ((49)) reproducing the main statistical properties of the absolute return, observed in the ﬁnancial markets. Seven parameters of the model enable us to adjust it to the sophisticated power-law statistics of various stocks including long-range behavior....

We scale and analyze the empirical data of return from New York and Vilnius stock exchanges matching it to the same nonlinear double stochastic model of return in financial market.

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from...

We present generalization of the point process models for the Poissonian-like processes with slowly diffusing mean interevent time and adjust the parameters of the model to the empirical data of trading activity and volatility in the ﬁnancial markets, reproducing the probability density function (PDF) and the power spectral density
(PSD).