6,314 research outputs found
Multifractal Height Cross-Correlation Analysis: A New Method for Analyzing Long-Range Cross-Correlations
We introduce a new method for detection of long-range cross-correlations and
multifractality - multifractal height cross-correlation analysis (MF-HXA) -
based on scaling of qth order covariances. MF-HXA is a bivariate generalization
of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L.,
Vicsek, T.: Multifractality of self-affine fractals, Physical Review A 44(4),
1991]. The method can be used to analyze long-range cross-correlations and
multifractality between two simultaneously recorded series. We illustrate a
power of the method on both simulated and real-world time series.Comment: 6 pages, 4 figure
SPITZER observations of the λ Orionis cluster. II. Disks around solar-type and low-mass stars
We present IRAC/MIPS Spitzer Space Telescope observations of the solar-type and the low-mass stellar population
of the young (~5Myr) λ Orionis cluster. Combining optical and Two Micron All Sky Survey photometry, we identify
436 stars as probable members of the cluster. Given the distance (450 pc) and the age of the cluster, our sample
ranges in mass from 2 M_⊙ to objects below the substellar limit. With the addition of the Spitzer mid-infrared data,
we have identified 49 stars bearing disks in the stellar cluster. Using spectral energy distribution slopes, we place
objects in several classes: non-excess stars (diskless), stars with optically thick disks, stars with “evolved disks”
(with smaller excesses than optically thick disk systems), and “transitional disk” candidates (in which the inner
disk is partially or fully cleared). The disk fraction depends on the stellar mass, ranging from ~6% for K-type stars (R_C − J 4). We confirm the dependence of disk
fraction on stellar mass in this age range found in other studies. Regarding clustering levels, the overall fraction of disks in the λ Orionis cluster is similar to those reported in other stellar groups with ages normally quoted as ~5Myr
Wavelet versus Detrended Fluctuation Analysis of multifractal structures
We perform a comparative study of applicability of the Multifractal Detrended
Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM)
method in proper detecting of mono- and multifractal character of data. We
quantify the performance of both methods by using different sorts of artificial
signals generated according to a few well-known exactly soluble mathematical
models: monofractal fractional Brownian motion, bifractal Levy flights, and
different sorts of multifractal binomial cascades. Our results show that in
majority of situations in which one does not know a priori the fractal
properties of a process, choosing MFDFA should be recommended. In particular,
WTMM gives biased outcomes for the fractional Brownian motion with different
values of Hurst exponent, indicating spurious multifractality. In some cases
WTMM can also give different results if one applies different wavelets. We do
not exclude using WTMM in real data analysis, but it occurs that while one may
apply MFDFA in a more automatic fashion, WTMM has to be applied with care. In
the second part of our work, we perform an analogous analysis on empirical data
coming from the American and from the German stock market. For this data both
methods detect rich multifractality in terms of broad f(alpha), but MFDFA
suggests that this multifractality is poorer than in the case of WTMM.Comment: substantially extended version, to appear in Phys.Rev.
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
Fractal Markets Hypothesis and the Global Financial Crisis: Scaling, Investment Horizons and Liquidity
We investigate whether fractal markets hypothesis and its focus on liquidity
and invest- ment horizons give reasonable predictions about dynamics of the
financial markets during the turbulences such as the Global Financial Crisis of
late 2000s. Compared to the mainstream efficient markets hypothesis, fractal
markets hypothesis considers financial markets as com- plex systems consisting
of many heterogenous agents, which are distinguishable mainly with respect to
their investment horizon. In the paper, several novel measures of trading
activity at different investment horizons are introduced through scaling of
variance of the underlying processes. On the three most liquid US indices -
DJI, NASDAQ and S&P500 - we show that predictions of fractal markets hypothesis
actually fit the observed behavior quite well.Comment: 11 pages, 3 figure
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