Analysis of price fluctuations in futures exchange markets

Lim, Gyuchang; Kim, SooYong; Scalas, Enrico; Kim, Kyungsik; Chang, Ki-Ho

doi:10.1016/j.physa.2008.01.040

Cited by 9 publications

(4 citation statements)

References 12 publications

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“…Non-vanishing higher-order (>2) KM coefficients, however, have been observed in various systems 3 15 19 20 21 22 , which indicates that the corresponding measured time series do not belong to the class of continuous diffusion processes 1 2 . In order to improve modelling of such processes, we argue that if all the conditional moments of KM coefficients of order larger than two are non-vanishing, jump events should play a significant role in the underlying stochastic process.…”

Section: Resultsmentioning

confidence: 99%

Disentangling the stochastic behavior of complex time series

Anvari

Tabar

Peinke

et al. 2016

Sci Rep

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Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events – or jumps – with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different stochastic behaviors, namely diffusive and jumpy ones, and show that all of the unknown functions and coefficients of this modelling can be derived directly from measured time series. We demonstrate appli- cability of our method to empirical observations by a data-driven inference of the deterministic drift term and of the diffusive and jumpy behavior in brain dynamics from ten epilepsy patients. Particularly these different stochastic behaviors provide extra information that can be regarded valuable for diagnostic purposes.

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Section: Resultsmentioning

confidence: 99%

Disentangling the stochastic behavior of complex time series

Anvari

Tabar

Peinke

et al. 2016

Sci Rep

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“…The KM expansion for the probability density of some stochastic process can be reduced to the Fokker-Planck equation if higher-order (>2) KM coefficients vanish. There are, however, many physical experiments that indicate non-vanishing higher-order KM coefficients [17,[32][33][34][35][36][37][38][39]. A priori, it is not evident if such observations are due to the finiteness of the respective sampling intervals or whether the measured time series do not belong to the class of continuous diffusion processes [14,40] and contain discontinuous, abrupt changes or jumps.…”

Section: Discussionmentioning

confidence: 99%

Characterizing abrupt transitions in stochastic dynamics

2018

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Data sampled at discrete times appears as a succession of discontinuous jumps, even if the underlying trajectory is continuous. We analytically derive a criterion that allows one to check whether for a given, even noisy time series the underlying process has a continuous (diffusion) trajectory or has jump discontinuities. This enables one to detect and characterize abrupt changes (jump events) in given time series. The proposed criterion is validated numerically using synthetic continuous and discontinuous time series. We demonstrate applicability of our criterion to distinguish diffusive and jumpy behavior by a data-driven inference of higher-order conditional moments from empirical observations.

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“…Such an expansion is admittedly questionable in view of Pawula's theorem, but can be controlled when manipulated with care (Popescu and Lipan, 2015). Thus, the theorem of Pawula does not necessarily restrict the truncation of higher order terms, when we can formally obtain high-order perturbative equations (Kanasava, 2017) and nonvanishing higher-order coefficients have been observed in various systems (Anvari et al, 2016;Friedrich et al;, 2011;Prusseit and Lehnertz, 2007;Tutkun and Mydlarski, 2004;Kim et al, 2008;Petelczyc et al, 2009Petelczyc et al, , 2015. Therefore, though higher-order perturbative models might, in some cases, have negative values at some isolated times and positions, this does not invalidate the models derived in the study, which are valid only in zones where large concentration gradients are applied.…”

Section: Discussionmentioning

confidence: 99%

Advection–Diffusion in Porous Media with Low Scale Separation: Modelling via Higher-Order Asymptotic Homogenisation

Royer

2019

Transp Porous Med

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Asymptotic multiple scale homogenisation allows to determine the effective behaviour of a porous medium by starting from the pore-scale description, when there is a large separation between the pore-scale and the macroscopic scale. When the scale ratio is "small but not too small," the standard approach based on firstorder homogenisation may break down since additional terms need to be taken into account in order to obtain an accurate picture of the overall response of the medium. The effect of low scale separation can be obtained by exploiting higher order equations in the asymptotic homogenisation procedure. The aim of the present study is to investigate higher-order terms up to the third order of the advectivediffusive model to describe advection-diffusion in a macroscopically homogeneous porous medium at low scale separation. The main result of the study is that the low separation of scales induces dispersion effects. In particular, the second-order model is similar to the most currently used phenomenological model of dispersion: it is characterised by a dispersion tensor which can be decomposed into a purely diffusive component and a mechanical dispersion part, whilst this property is not verified in the homogenised dispersion model (obtained at higher Péclet number). The third-order description contains second and third concentration gradient terms, with a fourth order tensor of diffusion and with a third-order and an additional second-order tensors of dispersion. The analysis of the macroscopic fluxes shows that the second and the third order macroscopic fluxes are distinct from the volume averages of the corresponding local fluxes and allows to determine expressions of the non-local effects.

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Analysis of price fluctuations in futures exchange markets

Cited by 9 publications

References 12 publications

Disentangling the stochastic behavior of complex time series

Disentangling the stochastic behavior of complex time series

Characterizing abrupt transitions in stochastic dynamics

Advection–Diffusion in Porous Media with Low Scale Separation: Modelling via Higher-Order Asymptotic Homogenisation

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