66 research outputs found
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
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
The components of empirical multifractality in financial returns
We perform a systematic investigation on the components of the empirical
multifractality of financial returns using the daily data of Dow Jones
Industrial Average from 26 May 1896 to 27 April 2007 as an example. The
temporal structure and fat-tailed distribution of the returns are considered as
possible influence factors. The multifractal spectrum of the original return
series is compared with those of four kinds of surrogate data: (1) shuffled
data that contain no temporal correlation but have the same distribution, (2)
surrogate data in which any nonlinear correlation is removed but the
distribution and linear correlation are preserved, (3) surrogate data in which
large positive and negative returns are replaced with small values, and (4)
surrogate data generated from alternative fat-tailed distributions with the
temporal correlation preserved. We find that all these factors have influence
on the multifractal spectrum. We also find that the temporal structure (linear
or nonlinear) has minor impact on the singularity width of the
multifractal spectrum while the fat tails have major impact on ,
which confirms the earlier results. In addition, the linear correlation is
found to have only a horizontal translation effect on the multifractal spectrum
in which the distance is approximately equal to the difference between its DFA
scaling exponent and 0.5. Our method can also be applied to other financial or
physical variables and other multifractal formalisms.Comment: 6 epl page
Quantitative features of multifractal subtleties in time series
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the
Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of
multifractality in the time series. Series fluctuating according to a qGaussian
distribution, both uncorrelated and correlated in time, are used. For the
uncorrelated series at the border (q=5/3) between the Gaussian and the Levy
basins of attraction asymptotically we find a phase-like transition between
monofractal and bifractal characteristics. This indicates that these may solely
be the specific nonlinear temporal correlations that organize the series into a
genuine multifractal hierarchy. For analyzing various features of
multifractality due to such correlations, we use the model series generated
from the binomial cascade as well as empirical series. Then, within the
temporal ranges of well developed power-law correlations we find a fast
convergence in all multifractal measures. Besides of its practical significance
this fact may reflect another manifestation of a conjectured q-generalized
Central Limit Theorem
Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise
The paper is concerned with spatial and time regularity of solutions to
linear stochastic evolution equation perturbed by L\'evy white noise "obtained
by subordination of a Gaussian white noise". Sufficient conditions for spatial
continuity are derived. It is also shown that solutions do not have in general
\cadlag modifications. General results are applied to equations with fractional
Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already
been publishe
A Multifractal Analysis of Asian Foreign Exchange Markets
We analyze the multifractal spectra of daily foreign exchange rates for
Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar
from 1991 to 2005. We find that the return time series show multifractal
spectrum features for all four cases. To observe the effect of the Asian
currency crisis, we also estimate the multifractal spectra of limited series
before and after the crisis. We find that the Korean and Thai foreign exchange
markets experienced a significant increase in multifractality compared to
Hong-Kong and Japan. We also show that the multifractality is stronge related
to the presence of high values of returns in the series
The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation
We consider stochastic differential equation involving pathwise integral with
respect to fractional Brownian motion. The estimates for the Hurst parameter
are constructed according to first- and second-order quadratic variations of
observed values of the solution. The rate of convergence of these estimates to
the true value of a parameter is established.Comment: 20 page
The -boundedness of a family of integral operators on UMD Banach function spaces
We prove the -boundedness of a family of integral operators with an
operator-valued kernel on UMD Banach function spaces. This generalizes and
simplifies earlier work by Gallarati, Veraar and the author, where the
-boundedness of this family of integral operators was shown on Lebesgue
spaces. The proof is based on a characterization of -boundedness as
weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665
Quantum Iterated Function Systems
Iterated functions system (IFS) is defined by specifying a set of functions
in a classical phase space, which act randomly on an initial point. In an
analogous way, we define a quantum iterated functions system (QIFS), where
functions act randomly with prescribed probabilities in the Hilbert space. In a
more general setting a QIFS consists of completely positive maps acting in the
space of density operators. We present exemplary classical IFSs, the invariant
measure of which exhibits fractal structure, and study properties of the
corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005)], an exact solution was reported for the probability p_{n,k} to find exactly k real eigenvalues in the spectrum of an nxn real asymmetric matrix drawn at
random from Ginibre's Orthogonal Ensemble (GinOE). In the present paper, we offer a detailed derivation of the above result by concentrating on the proof of the Pfaffian integration theorem, the
key ingredient of our analysis of the statistics of real eigenvalues in the GinOE. We also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a
GinOE matrix restricted to have exactly k real eigenvalues. In the particular case of k=0, all correlation functions of complex eigenvalues are determined
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