324 research outputs found
On discrete stochastic processes with long-lasting time dependence
In this manuscript, we analytically and numerically study statistical
properties of an heteroskedastic process based on the celebrated ARCH generator
of random variables whose variance is defined by a memory of
-exponencial, form (). Specifically, we inspect
the self-correlation function of squared random variables as well as the
kurtosis. In addition, by numerical procedures, we infer the stationary
probability density function of both of the heteroskedastic random variables
and the variance, the multiscaling properties, the first-passage times
distribution, and the dependence degree. Finally, we introduce an asymmetric
variance version of the model that enables us to reproduce the so-called
leverage effect in financial markets.Comment: 24 page
Are all highly liquid securities within the same class?
In this manuscript we analyse the leading statistical properties of
fluctuations of (log) 3-month US Treasury bill quotation in the secondary
market, namely: probability density function, autocorrelation, absolute values
autocorrelation, and absolute values persistency. We verify that this financial
instrument, in spite of its high liquidity, shows very peculiar properties.
Particularly, we verify that log-fluctuations belong to the Levy class of
stochastic variables.Comment: To be published in EPJ
On superstatistical multiplicative-noise processes
In this manuscript we analyse the long-term probability density function of
non-stationary dynamical processes which are enclosed inward the Feller class
of processes with time varying exponents for multiplicative noise. The update
in the value of the exponent occurs in the same conditions presented by Beck
and Cohen for superstatistics. Moreover, we are able to provide a dynamical
scenario for the emergence of a generalisation of the Weibull distribution
previously introduced.Comment: 7 pages, 8 figures. A note about the application on turbulence models
has been added to this final published versio
Edge of chaos of the classical kicked top map: Sensitivity to initial conditions
We focus on the frontier between the chaotic and regular regions for the
classical version of the quantum kicked top. We show that the sensitivity to
the initial conditions is numerically well characterised by , where , and
is the -generalization of the Lyapunov coefficient, a result
that is consistent with nonextensive statistical mechanics, based on the
entropy ). Our analysis
shows that monotonically increases from zero to unity when the kicked-top
perturbation parameter increases from zero (unperturbed top) to
, where . The entropic index remains equal
to unity for , parameter values for which the phase space
is fully chaotic.Comment: To appear in "Complexity, Metastability and Nonextensivity" (World
Scientific, Singapore, 2005), Eds. C. Beck, A. Rapisarda and C. Tsalli
Bridging stylized facts in finance and data non-stationarities
Employing a recent technique which allows the representation of nonstationary
data by means of a juxtaposition of locally stationary patches of different
length, we introduce a comprehensive analysis of the key observables in a
financial market: the trading volume and the price fluctuations. From the
segmentation procedure we are able to introduce a quantitative description of a
group of statistical features (stylizes facts) of the trading volume and price
fluctuations, namely the tails of each distribution, the U-shaped profile of
the volume in a trading session and the evolution of the trading volume
autocorrelation function. The segmentation of the trading volume series
provides evidence of slow evolution of the fluctuating parameters of each
patch, pointing to the mixing scenario. Assuming that long-term features are
the outcome of a statistical mixture of simple local forms, we test and compare
different probability density functions to provide the long-term distribution
of the trading volume, concluding that the log-normal gives the best agreement
with the empirical distribution. Moreover, the segmentation of the magnitude
price fluctuations are quite different from the results for the trading volume,
indicating that changes in the statistics of price fluctuations occur at a
faster scale than in the case of trading volume.Comment: 13 pages, 12 figure
- …