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

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1125
Author(s):  
Rytis Kazakevičius ◽  
Aleksejus Kononovicius ◽  
Bronislovas Kaulakys ◽  
Vygintas Gontis
Keyword(s):  
Financial Markets ◽  
Long Range ◽  
Markov Processes ◽  
Point Processes ◽  
First Passage Time ◽  
Moving Average ◽  
Social Systems ◽  
Passage Time ◽  
Stable Motion ◽  
Non Gaussian

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.

scholarly journals Understanding the Nature of the Long–Range Memory Phenomenon in Socio–Economic Systems

2021 ◽  
Author(s):  
Rytis Kazakevičius ◽  
Aleksejus Kononovicius ◽  
Bronislovas Kaulakys ◽  
Vygintas Gontis
Keyword(s):  
Financial Markets ◽  
Long Range ◽  
Markov Processes ◽  
Point Processes ◽  
Social Systems ◽  
Passage Time ◽  
Economic Systems ◽  
Gaussian Distributions ◽  
Stable Motion ◽  
The Face

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 actual long–range memory process or just a consequence of 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 ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

scholarly journals Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 634 ◽  
Author(s):  
Pietro Murialdo ◽  
Linda Ponta ◽  
Anna Carbone
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Long Range ◽  
Financial Time Series ◽  
Moving Average ◽  
Social Systems ◽  
Long Run ◽  
Characteristic Behaviour ◽  
Correlation Parameters ◽  
Average Cluster

A perspective is taken on the intangible complexity of economic and social systems by investigating the dynamical processes producing, storing and transmitting information in financial time series. An extensive analysis based on the moving average cluster entropy approach has evidenced market and horizon dependence in highest-frequency data of real world financial assets. The behavior is scrutinized by applying the moving average cluster entropy approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). An extensive set of series is generated with a broad range of values of the Hurst exponent H and of the autoregressive, differencing and moving average parameters p , d , q . A systematic relation between moving average cluster entropy and long-range correlation parameters H, d is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter d ≃ 0.05 , d ≃ 0.15 and d ≃ 0.25 are consistent with moving average cluster entropy results obtained in time series of DJIA, S&P500 and NASDAQ. The findings clearly point to a variability of price returns, consistently with a price dynamics involving multiple temporal scales and, thus, short- and long-run volatility components. An important aspect of the proposed approach is the ability to capture detailed horizon dependence over relatively short horizons (one to twelve months) and thus its relevance to define risk analysis indices.

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

1987 ◽  
Vol 1 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Mark Brown ◽  
Yi-Shi Shao
Keyword(s):  
Markov Processes ◽  
Time Distribution ◽  
Infinitesimal Generator ◽  
Spectral Representation ◽  
First Passage Time ◽  
Passage Time ◽  
Spectral Approach ◽  
Generator Matrix ◽  
Eigenvalues And Eigenvectors ◽  
First Passage

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

scholarly journals Non-radial functions, nonlocal operators and Markov processes over p-adic numbers

2019 ◽  
Vol 24 (2) ◽  
pp. 381-406 ◽  
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Oscar Francisco Casas-Sánchez
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Parabolic Type ◽  
Passage Time ◽  
Fundamental Solutions ◽  
Nonlocal Operators ◽  
Transition Functions ◽  
Time Problem ◽  
The Cauchy Problem ◽  
First Passage Time Problem

The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition functions of Markov processes on an n-dimensional vector space over the p-adic numbers. We also study some properties of these Markov processes, including the first passage time problem.

scholarly journals A unified approach for drawdown (drawup) of time-homogeneous Markov processes

2017 ◽  
Vol 54 (2) ◽  
pp. 603-626 ◽  
Author(s):  
David Landriault ◽  
Bin Li ◽  
Hongzhong Zhang
Keyword(s):  
Markov Processes ◽  
Financial Risk ◽  
First Passage Time ◽  
Passage Time ◽  
Regularity Conditions ◽  
Unified Approach ◽  
First Passage ◽  
Underlying Process ◽  
Short Time ◽  
General Time

AbstractDrawdown (respectively, drawup) of a stochastic process, also referred as the reflected process at its supremum (respectively, infimum), has wide applications in many areas including financial risk management, actuarial mathematics, and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of the first passage time of the drawdown (respectively, drawup) process, its overshoot, and the maximum of the underlying process at this first passage time. By using short-time pathwise analysis, under some mild regularity conditions, the joint law of the three drawdown quantities is shown to be the unique solution to an integral equation which is expressed in terms of fundamental two-sided exit quantities of the underlying process. Explicit forms for this joint law are found when the Markov process has only one-sided jumps or is a Lévy process (possibly with two-sided jumps). The proposed methodology provides a unified approach to study various drawdown quantities for the general class of time-homogeneous Markov processes.

A computational approach to first-passage-time problems for Gauss–Markov processes

2001 ◽  
Vol 33 (2) ◽  
pp. 453-482 ◽  
Author(s):  
E. Di Nardo ◽  
A. G. Nobile ◽  
E. Pirozzi ◽  
L. M. Ricciardi
Keyword(s):  
Markov Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Computational Approach ◽  
First Passage ◽  
First Passage Time Problems

scholarly journals First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises

2021 ◽  
Author(s):  
Nicholas Mwilu Mutothya ◽  
Yong Xu ◽  
Yongge Li ◽  
Ralf Metzler ◽  
Nicholas Muthama Mutua
Keyword(s):  
Diffusion Coefficient ◽  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Stochastic Motion ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Markovian Systems

Abstract We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' $q$-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times are recorded. The first passage time density is determined along with the mean first passage time. Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the mean first passage time are discussed.

scholarly journals A Symmetry-Based Approach for First-Passage-Times of Gauss-Markov Processes through Daniels-Type Boundaries

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 279
Author(s):  
Enrica Pirozzi
Keyword(s):  
Probability Density ◽  
Markov Processes ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Transition Probability ◽  
Passage Time ◽  
First Passage ◽  
Transition Probability Density ◽  
Symmetry Properties ◽  
Time Density

Symmetry properties of the Brownian motion and of some diffusion processes are useful to specify the probability density functions and the first passage time density through specific boundaries. Here, we consider the class of Gauss-Markov processes and their symmetry properties. In particular, we study probability densities of such processes in presence of a couple of Daniels-type boundaries, for which closed form results exit. The main results of this paper are the alternative proofs to characterize the transition probability density between the two boundaries and the first passage time density exploiting exclusively symmetry properties. Explicit expressions are provided for Wiener and Ornstein-Uhlenbeck processes.

scholarly journals Universal First-Passage-Time Distribution of Non-Gaussian Currents

2019 ◽  
Vol 122 (23) ◽  
Author(s):  
Shilpi Singh ◽  
Paul Menczel ◽  
Dmitry S. Golubev ◽  
Ivan M. Khaymovich ◽  
Joonas T. Peltonen ◽  
...  
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Non Gaussian
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