International finance, Lévy distributions, and the econophysics of exchange rates

Silva, Sergio Da; Matsushita, Raul; Gleria, Iram; Figueiredo, Annibal; Rathie, Pushpa N.

doi:10.1016/j.cnsns.2003.12.001

Cited by 13 publications

(4 citation statements)

References 93 publications

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“…(Recall that the classical Central Limit Theorem states that the limit of normalized sums of independent identically distributed terms with finite variance is Gaussian.) The third argument for modeling with Lévy-stable distributions is empirical; many large data sets exhibit fat tails (or heavy tails); for a review see [42,43]. Such data sets were described by a Casting model based on the lognormal ansatz (in terms of the variance of the Gaussian distribution).…”

Section: L éVy Distribution Modelmentioning

confidence: 99%

Fractality feature in oil price fluctuations

Momeni,

Kourakis,

Talebi

2008

Preprint

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The scaling properties of oil price fluctuations are described as a non-stationary stochastic process realized by a time series of finite length. An original model is used to extract the scaling exponent of the fluctuation functions within a non-stationary process formulation. It is shown that, when returns are measured over intervals less than 10 days, the Probability Density Functions (PDFs) exhibit self-similarity and monoscaling, in contrast to the multifractal behavior of the PDFs at macro-scales (typically larger than one month). We find that the time evolution of the distributions are well fitted by a Lévy distribution law at micro-scales. The relevance of a Lévy distribution is made plausible by a simple model of nonlinear transfer.

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Section: L éVy Distribution Modelmentioning

confidence: 99%

Fractality feature in oil price fluctuations

Momeni,

Kourakis,

Talebi

2008

Preprint

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“…In general, all have a fractal nature with variations that are difficult to predict [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ]. A number of techniques have been proposed to investigate the financial indices and to unravel the embedded complex dynamics [ 14 , 15 , 16 , 17 , 18 ]. Such studies adopt the underlying concept of linear time flow and consider that the fractal nature of the index is intrinsic to its own artificial nature.…”

Section: Introductionmentioning

confidence: 99%

Fractal and Entropy Analysis of the Dow Jones Index Using Multidimensional Scaling

Machado

2020

Entropy

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Financial time series have a fractal nature that poses challenges for their dynamical characterization. The Dow Jones Industrial Average (DJIA) is one of the most influential financial indices, and due to its importance, it is adopted as a test bed for this study. The paper explores an alternative strategy to the standard time analysis, by joining the multidimensional scaling (MDS) computational tool and the concepts of distance, entropy, fractal dimension, and fractional calculus. First, several distances are considered to measure the similarities between objects under study and to yield proper input information to the MDS. Then, the MDS constructs a representation based on the similarity of the objects, where time can be viewed as a parametric variable. The resulting plots show a complex structure that is further analyzed with the Shannon entropy and fractal dimension. In a final step, a deeper and more detailed assessment is achieved by associating the concepts of fractional calculus and entropy. Indeed, the fractional-order entropy highlights the results obtained by the other tools, namely that the DJIA fractal nature is visible at different time scales with a fractional order memory that permeates the time series.

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“…There are many financial indices for capturing the characteristics and evolution of different markets and stock exchange institutions, but it is well known that, in general, they all have a fractal nature with variations difficult to preview [6,[10][11][12][13][14][15][16][17]. Different approaches have been proposed to analyse these objects in order to master the complex dynamics [4,9,19,20,22], but all have in common the underlying undisputed concept of linear time flow. This paper studies the interplay between the evolution of FTS and the flow of time.…”

Section: Introductionmentioning

confidence: 99%