Computer Simulations with Mathematica: Explorations in Complex Physical and Biological Systems

Gaylord, Richard J.; Wellin, Paul R.; Titus, Bill; McKay, Susan R.; Christian, Wolfgang

doi:10.1063/1.4822455

Cited by 33 publications

(31 citation statements)

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“…[2,10,[12][13][14][15]. Recent empirical works have reported that the empirical probability distributions of financial returns are believed to deviate from a Gaussian distribution, and they usually exhibit more leptokurtic and fatter tails than the Gaussian case, which is usually called "fat-tail" distribution, and may be explained as the result of the herd effect of investors in the security markets or illiquidity.…”

Section: Basic Statistical Properties Of Returnsmentioning

confidence: 99%

“…Recently, much effort has gone into the study of reproducing and investigating nonlinear complex dynamics of financial systems for a further understanding the mechanisms of financial markets, and its crucial application in risk management, non-equilibrium derivatives pricing, hedging, forecasting, etc. [2,10,[12][13][14][15]. Over the past decade, a considerable volume of agent-based models have been proposed, based on the field of interacting particle systems (or statistical physics systems), to model the main observed stylized facts, such as fat-tailed distribution, volatility clustering, time-dependence, multifractality and complex dynamics [10,[16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

Wang

Zheng

Zhang

et al. 2017

Entropy

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This paper investigates the complex behaviors and entropy properties for a novel random complex interacting stock price dynamics, which is established by the combination of stochastic contact process and compound Poisson process, concerning with stock return fluctuations caused by the spread of investors' attitudes and random jump fluctuations caused by the macroeconomic environment, respectively. To better understand the fluctuation complex behaviors of the proposed price dynamics, the entropy analyses of random logarithmic price returns and corresponding absolute returns of simulation dataset with different parameter set are preformed, including permutation entropy, fractional permutation entropy, sample entropy and fractional sample entropy. We found that a larger λ or γ leads to more complex dynamics, and the absolute return series exhibit lower complex dynamics than the return series. To verify the rationality of the proposed compound price model, the corresponding analyses of actual market datasets are also comparatively preformed. The empirical results verify that the proposed price model can reproduce some important complex dynamics of actual stock markets to some extent.

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Section: Basic Statistical Properties Of Returnsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

Wang

Zheng

Zhang

et al. 2017

Entropy

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“…The corresponding stock logarithmic return and absolute return from t − 1 to t are defined by: According to the above definition and description of the model, we perform the simulation of stock price series and return series with different values of the parameters [45,46], finite-range R and intensity λ in the voter dynamic system. We set the number of traders M = 500 and the initial density of the model θ = 0.01.…”

Section: Price Process Modeling By a Finite-range Voter Systemmentioning

confidence: 99%

Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System

Niu

Wang

2015

Entropy

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A financial time series agent-based model is reproduced and investigated by the statistical physics system, the finite-range interacting voter system. The voter system originally describes the collective behavior of voters who constantly update their positions on a particular topic, which is a continuous-time Markov process. In the proposed model, the fluctuations of stock price changes are attributed to the market information interaction amongst the traders and certain similarities of investors' behaviors. Further, the complexity of return series of the financial model is studied in comparison with two real stock indexes, the Shanghai Stock Exchange Composite Index and the Hang Seng Index, by composite multiscale entropy analysis and recurrence analysis. The empirical research shows that the simulation data for the proposed model could grasp some natural features of actual markets to some extent.

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“…Ref. [15]). In order to make a concrete model we assume that the sound produced from a car at the site of the detection device leads to a sound-level L(t) = log(2 + v(t)), where v(t) is the velocity of the car at the site in lattice units per unit time.…”

Section: Wavelet Analysis Of Traffic Flow Datamentioning

confidence: 99%

Memory effects and scaling properties of traffic flows

Skagerstam¹,

Hansen²

2005

Europhys. Lett.

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Traffic flows are studied in terms of their noise of sound, which is an easily accessible experimental quantity. The sound noise data is studied making use of scaling properties of wavelet transforms and Hurst exponents are extracted. The scaling behavior is used to characterize the traffic flows in terms of scaling properties of the memory function in Mori-Lee stochastic differential equations. The results obtained provides for a new theoretical as well as experimental framework to characterize the large-time behavior of traffic flows. The present paper outlines the procedure by making use of one-lane computer simulations as well as sound-data measurements from a real two-lane traffic flow. We find the presence of conventional diffusion as well as 1/f noise in real traffic flows at large time scales.

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Computer Simulations with Mathematica: Explorations in Complex Physical and Biological Systems

Cited by 33 publications

References 0 publications

Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump

Entropy and Recurrence Measures of a Financial Dynamic System by an Interacting Voter System

Memory effects and scaling properties of traffic flows

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