共查询到20条相似文献,搜索用时 31 毫秒
1.
Fotios M. Siokis 《Physica A》2012,391(4):1315-1322
This paper presents a brief analysis on the distribution of magnitude of major stock market shocks. Based on the Gutenberg-Richter law in geophysics, we model the dynamics of market index returns prior and after major crashes in search of statistical regularities. For a large number of market crashes, our analysis suggests that the distribution of market volatility before and after the stock market crash is described well by the Gutenberg-Richter law, which reflects the scale-invariance and self-similarity of the underlying dynamics by a robust power-law relation. In addition, the rate of the decay of the aftershock sequence is well described by another power law, which is known as the Omori law. Power law relaxation seems to be a common behavior observed in complex systems such as the financial markets. 相似文献
2.
Sergio Picoli Fernando J. Antonio Andreia S. Itami Renio S. Mendes 《The European Physical Journal B - Condensed Matter and Complex Systems》2017,90(8):156
We study relaxation patterns of violent conflicts after bursts of activity. Data were obtained from available catalogs on the conflicts in Iraq, Afghanistan and Northern Ireland. We find several examples in each catalog for which the observed relaxation curves can be well described by an asymptotic power-law decay (the analog of the Omori’s law in geophysics). The power-law exponents are robust, nearly independent of the conflict. We also discuss the exogenous or endogenous nature of the shocks. Our results suggest that violent conflicts share with earthquakes and other natural and social phenomena a common feature in the dynamics of aftershocks. 相似文献
3.
The statistical properties of earthquake aftershocks are studied. The scaling relation for exponents of the Omori law and the power-law calm time distribution (i.e., the interoccurrence time distribution), which is valid if a sequence of aftershocks is a singular Markovian process, is carefully examined. Data analysis shows significant violation of the scaling relation, implying the non-Markovian nature of aftershocks. 相似文献
4.
M.W. Lee D. Sornette 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(1):193-197
Numerical simulations and a mean-field analysis of a sandpile model of earthquake aftershocks in 1d, 2d and 3d Euclidean lattices
determine that the average stress decays in a punctuated fashion after a main shock, with events occurring at characteristic
times increasing as a geometrical series with a well-defined multiplicative factor which is a function of the stress corrosion
exponent, the stress drop ratio and the degree of dissipation. These results are independent of the discrete nature of the
lattice and stem from the interplay between the threshold dynamics and the power law stress relaxation. This novel mechanism
of log-periodicity does not rely on a pre-existing discrete structural hierarchy of faults but is dynamical and reflects the
existence of an approximately fixed stress drop together with the scale-free stress corrosion power law acting during inter-seismic
phases.
Received 24 November 1999 相似文献
5.
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail. 相似文献
6.
Unified scaling law for earthquakes 总被引:2,自引:0,他引:2
We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d(f) of earthquakes appear as critical indices. 相似文献
7.
A. Svorenčík F. Slanina 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(4):453-462
Inspired by order-book models of financial fluctuations, we
investigate the Interacting gaps model, which is the schematic
one-dimensional system mimicking the order-book dynamics. We find by
simulations the power-law tail in return distribution, power-law decay
of volatility autocorrelation with exponent 0.5 and Hurst exponent
close to 1/2. Surprisingly, when we make a mean-field
approximation, i.e. replace the one-dimensional system by
effectively infinite-dimensional one, we obtain analytically the
return exponent 5/2, in perfect accord with one-dimensional simulations. 相似文献
8.
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 the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE. 相似文献
9.
The Hall-Petch (HP) law, that accounts for the effect of grain size on the plastic yield stress of polycrystals, is revisited in terms of the collective motion of interacting dislocations. Sudden relaxation of incompatibility stresses in a grain triggers aftershocks in the neighboring ones. The HP law results from a scaling argument based on the conservation of the elastic energy during such transfers. The Hall-Petch law breakdown for nanometric sized grains is shown to stem from the loss of such a collective behavior as grains start deforming by successive motion of individual dislocations. 相似文献
10.
Evaporative cooling of trapped atoms is described as a sequence of truncation of the high-energy tail of the thermal distribution followed by collisional relaxation. This model is solved analytically for arbitrary power-law potentials. The threshold density for accelerated evaporation is. found to be lowest in a three-dimensional linear potential.Dedicated to H. Walther on the occasion of his 60th birthday 相似文献
11.
In this work, we graft the volatility clustering observed in empirical financial time series into the Equiluz and Zimmermann (EZ) model, which was introduced to reproduce the herding behaviors of a financial time series. The original EZ model failed to reproduce the empirically observed power-law exponents of real financial data. The EZ model ordinarily produces a more fat-tailed distribution compared to real data, and a long-range correlation of absolute returns that underlie the volatility clustering. As it is not appropriate to capture the empirically observed correlations in a modified EZ model, we apply a sorting method to incorporate the nonlinear correlation structure of a real financial time series into the generated returns. By doing so, we observe that the slow convergence of distribution of returns is well established for returns generated from the EZ model and its modified version. It is also found that the modified EZ model leads to a less fat-tailed distribution. 相似文献
12.
X. Lei 《The European physical journal. Special topics》2012,205(1):217-230
In order to shed some lights to the “dragon-kings” concept, this paper re-examines experimental results on rock fracture tests
in the laboratory, obtained from acoustic emission monitoring. The fracture of intact rocks as well as rocks containing natural
structures (joints, faults, foliations) under constant stress rate loading or creep conditions is generally characterized
by typical stages with different underlying physics. The primary phase reflects the initial rupture of pre-existing microcrack
population in the sample or in the fault zone. Sub-critical growth dominates the secondary phase. The third phases termed
nucleation phase corresponds to the initiation and accelerated growth of the ultimate fracture. The secondary and nucleation
phases in both intact rock and faulted rock show power-law (of time-to-failure) increasing event rate and moment release.
Samples containing planar structures such as foliations and faults demonstrate very similar features to natural earthquakes
including: 1) small number of immediate foreshocks by which fault nucleation zones could be mapped; 2) the critical nucleation
zone size is normally a fraction of the sample dimension; 3) a lot of aftershocks concentrated on the fault ruptured during
the main event; 4) stress drop due to the main rupture is of the order from a few tens to a few hundreds MPa; 5) b-value drops during foreshocks and recovers during the aftershocks. All these results agree with the suggestion that laboratory
measurements require no scaling but can be applied directly to the Earth to represent local fault behavior. The ultimate failure
of the sample, or fracture of major asperities on the fault surface, normally lead to extreme events, i.e., dragon-kings,
which has a magnitude significantly greater than that expected by the Gutenberg-Richter power-law relation in the magnitude-frequency
distribution for either foreshocks or aftershocks. There are at least two mechanisms that may lead to dragon-kings: 1) The
power-law increasing event rate and moment release; and 2) Hierarchical fracturing behavior resulting from hierarchical inhomogeneities
in the sample. In the 1st mechanism, the final failure corresponds to the end point of the progressive occurrence of events
and thus the resulted dragon-king event can be interpreted as a superposition of many small events. While for the 2nd mechanism
an event of extreme size is the result of fracture growth stepping from a lower hierarchy into a higher hierarchy on fault
surface having asperities characterized by hierarchical distribution (of size or strength) rather than simple fractal distribution.
In both mechanisms the underlying physics is that fracture in rocks is hard to stop beyond certain threshold corresponding
to the critical nucleation zone size. 相似文献
13.
We present creep experiments on fiber composite materials with different controlled heterogeneity. All samples exhibit a power-law relaxation of the strain rate in the primary creep regime (Andrade's law) followed by a power-law acceleration up to rupture. We discover that the rupture time is proportional to the duration of the primary creep regime, showing the interplay between the two regimes and offering a method of rupture prediction. These experimental results are rationalized by a mean-field model of representative elements with nonlinear viscoelastic rheology and with a large heterogeneity of strengths. 相似文献
14.
Clustering of volatility as a multiscale phenomenon 总被引:3,自引:0,他引:3
M. Pasquini M. Serva 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(1):195-201
The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically
(models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What is well known is that
absolute returns have memory on a long time range, this phenomenon is known as clustering of volatility. In this paper we
show that volatility correlations are power-laws with a non-unique scaling exponent. This kind of multiscale phenomenology
has some analogies with fully developed turbulence and disordered systems and it is now pointed out for financial series.
Starting from historical returns series, we have also derived the volatility distribution, and the results are in agreement
with a log-normal shape. In our study, we consider the New York Stock Exchange (NYSE), daily composite index closes (January
1966 to June 1998) and the US Dollar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New
York (October 1989 to September 1998).
Received 1 February 2000 相似文献
15.
A cosmic acceleration mechanism is introduced which is based on the wakefields excited by the Alfvén shocks in a relativistically flowing plasma. We show that there exists a threshold condition for transparency below which the accelerating particle is collision-free and suffers little energy loss in the plasma medium. The stochastic encounters of the random accelerating-decelerating phases results in a power-law energy spectrum: f(epsilon) proportional, variant 1/epsilon(2). As an example, we discuss the possible production in the atmosphere of gamma ray bursts of ultrahigh-energy cosmic rays (UHECR) exceeding the Greisen-Zatsepin-Kuzmin cutoff. The estimated event rate in our model agrees with that from UHECR observations. 相似文献
16.
Stylized facts from a threshold-based heterogeneous agent model 总被引:1,自引:0,他引:1
R. Cross M. Grinfeld H. Lamba T. Seaman 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(2):213-218
A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to
do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by
the efficient market hypothesis (EMH).
By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their
effects upon the market dynamics.
The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay
consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible
alternatives for introducing such long-term volatility correlations are then identified and discussed. 相似文献
17.
Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the variance of the price fluctuations, with empirical characteristics. In particular we find its probability distribution is similar to a log normal distribution but with a long power-law tail for the large fluctuations, and that the time development shows superdiffusion. Both these results are in good quantitative agreement with observations. 相似文献
18.
19.
The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. We propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on minutely S&P 500 index from 1982 to 1999 and its inverse measure of exit time. Both the direct and inverse measures exhibit nice multifractal nature, whose sealing ranges are not irrelevant. Empirical investigation shows that the inversion formula holds in financial markets. 相似文献
20.
F. Wang P. Weber K. Yamasaki S. Havlin H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(2):123-133
We discuss recent results concerning statistical regularities in the
return intervals of volatility in financial markets. In particular, we
show how the analysis of volatility return intervals, defined as the
time between two volatilities larger than a given threshold, can help
to get a better understanding of the behavior of financial time
series. We find scaling in the distribution of return intervals for
thresholds ranging over a factor of 25, from 0.6 to 15 standard
deviations, and also for various time windows from one minute up to
390 min (an entire trading day). Moreover, these results are
universal for different stocks, commodities, interest rates as well as
currencies. We also analyze the memory in the return intervals which
relates to the memory in the volatility and find two scaling regimes,
ℓ<ℓ* with α1=0.64±0.02 and ℓ> ℓ*
with α2=0.92±0.04; these exponent values are similar to
results of Liu et al. for the volatility. As an application, we use
the scaling and memory properties of the return intervals to suggest a
possibly useful method for estimating risk. 相似文献