314 research outputs found
Log-periodic self-similarity: an emerging financial law?
A hypothesis that the financial log-periodicity, cascading self-similarity
through various time scales, carries signatures of a law is pursued. It is
shown that the most significant historical financial events can be classified
amazingly well using a single and unique value of the preferred scaling factor
lambda=2, which indicates that its real value should be close to this number.
This applies even to a declining decelerating log-periodic phase. Crucial in
this connection is identification of a "super-bubble" (bubble on bubble)
phenomenon. Identifying a potential "universal" preferred scaling factor, as
undertaken here, may significantly improve the predictive power of the
corresponding methodology. Several more specific related results include
evidence that: (i) the real end of the high technology bubble on the stock
market started (with a decelerating log-periodic draw down) in the begining of
September 2000; (ii) a parallel 2000-2002 decline seen in the Standard & Poor's
500 from the log-periodic perspective is already of the same significance as
the one of the early 1930s and of the late 1970s; (iii) all this points to a
much more serious global crash in around 2025, of course from a level much
higher (at least one order of magnitude) than in 2000.Comment: Talk given by S. Drozdz at International Econophysics Conference,
Bali, August 28-31, 2002; typos correcte
Decomposing the stock market intraday dynamics
The correlation matrix formalism is used to study temporal aspects of the
stock market evolution. This formalism allows to decompose the financial
dynamics into noise as well as into some coherent repeatable intraday
structures. The present study is based on the high-frequency Deutsche
Aktienindex (DAX) data over the time period between November 1997 and September
1999, and makes use of both, the corresponding returns as well as volatility
variations. One principal conclusion is that a bulk of the stock market
dynamics is governed by the uncorrelated noise-like processes. There exists
however a small number of components of coherent short term repeatable
structures in fluctuations that may generate some memory effects seen in the
standard autocorrelation function analysis. Laws that govern fluctuations
associated with those various components are different, which indicates an
extremely complex character of the financial fluctuations.Comment: 15 pages, 13 PostScript figure
Quantifying dynamics of the financial correlations
A novel application of the correlation matrix formalism to study dynamics of
the financial evolution is presented. This formalism allows to quantify the
memory effects as well as some potential repeatable intradaily structures in
the financial time-series. The present study is based on the high-frequency
Deutsche Aktienindex (DAX) data over the time-period between November 1997 and
December 1999 and demonstrates a power of the method. In this way two
significant new aspects of the DAX evolution are identified: (i) the memory
effects turn out to be sizably shorter than what the standard autocorrelation
function analysis seems to indicate and (ii) there exist short term repeatable
structures in fluctuations that are governed by a distinct dynamics. The former
of these results may provide an argument in favour of the market efficiency
while the later one may indicate origin of the difficulty in reaching a
Gaussian limit, expected from the central limit theorem, in the distribution of
returns on longer time-horizons.Comment: 10 pages, 7 PostScript figures, talk presented by the first Author at
the NATO ARW on Econophysics, Prague, February 8-10, 2001; to be published in
proceedings (Physica A
Quantum Monte Carlo calculation of the finite temperature Mott-Hubbard transition
We present clear numerical evidence for the coexistence of metallic and
insulating dynamical mean field theory(DMFT) solutions in a half-filled
single-band Hubbard model with bare semicircular density of states at finite
temperatures. Quantum Monte Carlo(QMC) method is used to solve the DMFT
equations. We discuss important technical aspects of the DMFT-QMC which need to
be taken into account in order to obtain the reliable results near the
coexistence region. Among them are the critical slowing down of the iterative
solutions near phase boundaries, the convergence criteria for the DMFT
iterations, the interpolation of the discretized Green's function and the
reduction of QMC statistical and systematic errors. Comparison of our results
with those of other numerical methods is presented in a phase diagram.Comment: 4 pages, 5 figure
Variety and Volatility in Financial Markets
We study the price dynamics of stocks traded in a financial market by
considering the statistical properties both of a single time series and of an
ensemble of stocks traded simultaneously. We use the stocks traded in the
New York Stock Exchange to form a statistical ensemble of daily stock returns.
For each trading day of our database, we study the ensemble return
distribution. We find that a typical ensemble return distribution exists in
most of the trading days with the exception of crash and rally days and of the
days subsequent to these extreme events. We analyze each ensemble return
distribution by extracting its first two central moments. We observe that these
moments are fluctuating in time and are stochastic processes themselves. We
characterize the statistical properties of ensemble return distribution central
moments by investigating their probability density functions and temporal
correlation properties. In general, time-averaged and portfolio-averaged price
returns have different statistical properties. We infer from these differences
information about the relative strength of correlation between stocks and
between different trading days. Lastly, we compare our empirical results with
those predicted by the single-index model and we conclude that this simple
model is unable to explain the statistical properties of the second moment of
the ensemble return distribution.Comment: 10 pages, 11 figure
Persistence Probabilities of the German DAX and Shanghai Index
We present a relatively detailed analysis of the persistence probability
distributions in financial dynamics. Compared with the auto-correlation
function, the persistence probability distributions describe dynamic
correlations non-local in time. Universal and non-universal behaviors of the
German DAX and Shanghai Index are analyzed, and numerical simulations of some
microscopic models are also performed. Around the fixed point , the
interacting herding model produces the scaling behavior of the real markets
Anomalous Diffusion in Aperiodic Environments
We study the Brownian motion of a classical particle in one-dimensional
inhomogeneous environments where the transition probabilities follow
quasiperiodic or aperiodic distributions. Exploiting an exact correspondence
with the transverse-field Ising model with inhomogeneous couplings we obtain
many new analytical results for the random walk problem. In the absence of
global bias the qualitative behavior of the diffusive motion of the particle
and the corresponding persistence probability strongly depend on the
fluctuation properties of the environment. In environments with bounded
fluctuations the particle shows normal diffusive motion and the diffusion
constant is simply related to the persistence probability. On the other hand in
a medium with unbounded fluctuations the diffusion is ultra-slow, the
displacement of the particle grows on logarithmic time scales. For the
borderline situation with marginal fluctuations both the diffusion exponent and
the persistence exponent are continuously varying functions of the
aperiodicity. Extensions of the results to disordered media and to higher
dimensions are also discussed.Comment: 11 pages, RevTe
A novel proviral clone of HIV-2: Biological and phylogenetic relationship to other primate immunodeficiency viruses.
Infectious molecular clones of the human immunodeficiency virus type 2 (HIV-2) will be valuable tools for the study of regulatory gene functions and the development of an animal model for the human acquired immunodeficiency syndrome (AIDS). To this end, we have cloned and sequenced a novel HIV-2 isolate, HIV-2BEN. One clone, designated MK6, is infectious for various human T-cell lines and for human and macaque peripheral blood lymphocytes (PBL), allowing molecular studies of HIV-2 infection and replication. Since MK6 is highly cytopathic in MT-2 and Molt-4 clone 8 cells, antiviral agents and neutralizing sera may be tested. Cluster analysis of HIV-1, HIV-2, and simian immunodeficiency virus (SIV) env and gag genes revealed that HIV-2BEN yielded the earliest node of phylogenetic divergence for all reported HIV-2 sequences. Noise analysis showed that, with the current data, no specification of any branching order can be made among the four groups of primate lentiviruses, HIV-1, HIV-2/SIVSMM/MAC, SIVAGM, and SIVMND
A New Method to Estimate the Noise in Financial Correlation Matrices
Financial correlation matrices measure the unsystematic correlations between
stocks. Such information is important for risk management. The correlation
matrices are known to be ``noise dressed''. We develop a new and alternative
method to estimate this noise. To this end, we simulate certain time series and
random matrices which can model financial correlations. With our approach,
different correlation structures buried under this noise can be detected.
Moreover, we introduce a measure for the relation between noise and
correlations. Our method is based on a power mapping which efficiently
suppresses the noise. Neither further data processing nor additional input is
needed.Comment: 25 pages, 8 figure
Surface metal-insulator transition in the Hubbard model
The correlation-driven metal-insulator (Mott) transition at a solid surface
is studied within the Hubbard model for a semi-infinite lattice by means of the
dynamical mean-field theory. The transition takes place at a unique critical
strength of the interaction. Depending on the surface geometry, the interaction
strength and the wave vector, we find one-electron excitations in the coherent
part of the surface-projected metallic spectrum which are confined to two
dimensions.Comment: LaTeX, 9 pages, 5 eps figures included, Phys. Rev. B (in press
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