The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect

Effect of detrending on multifractal characteristics

Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.Comment: Presented by P. O\'swi\k{e}cimka at FENS2012 conference, 17 pages, 9 figure

Spectral Decorrelation of Nuclear Levels in the Presence of Continuum Decay

The fluctuation properties of nuclear giant resonance spectra are studied in the presence of continuum decay. The subspace of quasi-bound states is specified by one-particle one-hole and two-particle two-hole excitations and the continuum coupling is generated by a scattering ensemble. It is found that, with increasing number of open channels, the real parts of the complex eigenvalues quickly decorrelate. This appears to be related to the transition from power-law to exponential time behavior of the survival probability of an initially non-stationary state.Comment: 10 Pages, REVTEX, 4 PostScript figure

Molecular dynamics approach: from chaotic to statistical properties of compound nuclei

Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the survival probability evolves to a limiting energy distribution whose density develops the Boltzmann form. The angular distribution of the corresponding decay products shows symmetry with respect to $\pi/2$ angle. Time estimated for the compound nucleus formation ranges within the order of $10^{-21}$s.Comment: 11 pages, LaTeX, non

Complex network analysis of literary and scientific texts

We present results from our quantitative study of statistical and network properties of literary and scientific texts written in two languages: English and Polish. We show that Polish texts are described by the Zipf law with the scaling exponent smaller than the one for the English language. We also show that the scientific texts are typically characterized by the rank-frequency plots with relatively short range of power-law behavior as compared to the literary texts. We then transform the texts into their word-adjacency network representations and find another difference between the languages. For the majority of the literary texts in both languages, the corresponding networks revealed the scale-free structure, while this was not always the case for the scientific texts. However, all the network representations of texts were hierarchical. We do not observe any qualitative and quantitative difference between the languages. However, if we look at other network statistics like the clustering coefficient and the average shortest path length, the English texts occur to possess more clustered structure than do the Polish ones. This result was attributed to differences in grammar of both languages, which was also indicated in the Zipf plots. All the texts, however, show network structure that differs from any of the Watts-Strogatz, the Barabasi-Albert, and the Erdos-Renyi architectures

Self-Similar Log-Periodic Structures in Western Stock Markets from 2000

The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work we analyze the daily closures of three of the most important indices worldwide since 2000: the DAX for Germany and the Nasdaq100 and the S&P500 for the United States. The qualitative behaviour of these different markets is similar during the temporal frame studied. Evidence is found for decelerating log-periodic oscillations of duration about two years and starting in September 2000. Moreover, a nested sub-structure starting in May 2002 is revealed, bringing more evidence to support the hypothesis of self-similar, log-periodic behavior. Ongoing log-periodic oscillations are also revealed. A Lomb analysis over the aforementioned periods indicates a preferential scaling factor $\lambda \sim 2$. Higher order harmonics are also present. The spectral pattern of the data has been found to be similar to that of a Weierstrass-type function, used as a prototype of a log-periodic fractal function.Comment: 17 pages, 14 figures. International Journal of Modern Physics C, in pres

On the energy-shell contributions of the three-particle~-~ three-hole excitations

The response functions for the extended second and third random phase approximation are compared. A second order perturbation calculation shows that the first-order amplitude for the direct $3p3h$ excitation from the ground state cancels with those that are engendered by the $1p1h$-$3p3h$ coupling. As a consequence nonvanishing $3p3h$ effects to the $1p1h$ response involve off energy shell renormalization only. On shell $3p3h$ processes are absent.Comment: 12 pages text (LaTex) and 1 figure included, to be published in Phys. Rev.

Stock mechanics: predicting recession in S&P500, DJIA, and NASDAQ

An original method, assuming potential and kinetic energy for prices and conservation of their sum is developed for forecasting exchanges. Connections with power law are shown. Semiempirical applications on S&P500, DJIA, and NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock Exchange index ISE-100 is found involving a potential to continue to rise.Comment: 14 pages, 4 figure

Momentum Distribution in Nuclear matter within a Perturbation Approximation

It is shown that the norm corrections, introduced to avoid the violation of the constraints on the depletion of the hole states in the standard perturbative 2p2h approach, leads in nuclear matter to a dependence of the momentum distribution with the total nucleon number. This unphysical behavior, which in turn makes the depletion to be non-extensive, arises from contributions of disconnected diagrams contained in the norm. It is found that the extensivity is again recovered when the 4p4h excitations in the ground state are included, and a reasonable value for the total number of nucleons promoted above the Fermi level is obtained.Comment: 11 pages, LaTeX, 5 figures, figures 1 to 3 included in the latex file, postscript files of figures 4 and 5 available from the Authors. Accepted for publication in Phys. Rev.