6 research outputs found
Nonextensive statistical features of the Polish stock market fluctuations
The statistics of return distributions on various time scales constitutes one
of the most informative characteristics of the financial dynamics. Here we
present a systematic study of such characteristics for the Polish stock market
index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging
from one minute up to one hour. This market is commonly classified as emerging.
Still on the shortest time scales studied we find that the tails of the return
distributions are consistent with the inverse cubic power-law, as identified
previously for majority of the mature markets. Within the time scales studied a
quick and considerable departure from this law towards a Gaussian can however
be traced. Interestingly, all the forms of the distributions observed can be
comprised by the single -Gaussians which provide a satisfactory and at the
same time compact representation of the distribution of return fluctuations
over all magnitudes of their variation. The corresponding nonextensivity
parameter is found to systematically decrease when increasing the time
scales.Comment: 14 pages. Physica A in prin
Stock market return distributions: from past to present
We show that recent stock market fluctuations are characterized by the
cumulative distributions whose tails on short, minute time scales exhibit power
scaling with the scaling index alpha > 3 and this index tends to increase
quickly with decreasing sampling frequency. Our study is based on
high-frequency recordings of the S&P500, DAX and WIG20 indices over the
interval May 2004 - May 2006. Our findings suggest that dynamics of the
contemporary market may differ from the one observed in the past. This effect
indicates a constantly increasing efficiency of world markets.Comment: to appear in Physica
Components of multifractality in high-frequency stock returns
We analyzed multifractal properties of 5-minute stock returns from a period
of over two years for 100 highly capitalized American companies. The two
sources: fat-tailed probability distributions and nonlinear temporal
correlations, vitally contribute to the observed multifractal dynamics of the
returns. For majority of the companies the temporal correlations constitute a
much more significant related factor, however.Comment: to appear in Physica
Multifractality in the stock market: price increments versus waiting times
By applying the multifractal detrended fluctuation analysis to the
high-frequency tick-by-tick data from Deutsche B\"orse both in the price and in
the time domains, we investigate multifractal properties of the time series of
logarithmic price increments and inter-trade intervals of time. We show that
both quantities reveal multiscaling and that this result holds across different
stocks. The origin of the multifractal character of the corresponding dynamics
is, among others, the long-range correlations in price increments and in
inter-trade time intervals as well as the non-Gaussian distributions of the
fluctuations. Since the transaction-to-transaction price increments do not
strongly depend on or are almost independent of the inter-trade waiting times,
both can be sources of the observed multifractal behaviour of the fixed-delay
returns and volatility. The results presented also allow one to evaluate the
applicability of the Multifractal Model of Asset Returns in the case of
tick-by-tick data.Comment: Physica A, in prin
Finite-size effect and the components of multifractality in financial volatility
Many financial variables are found to exhibit multifractal nature, which is
usually attributed to the influence of temporal correlations and fat-tailedness
in the probability distribution (PDF). Based on the partition function approach
of multifractal analysis, we show that there is a marked finite-size effect in
the detection of multifractality, and the effective multifractality is the
apparent multifractality after removing the finite-size effect. We find that
the effective multifractality can be further decomposed into two components,
the PDF component and the nonlinearity component. Referring to the normal
distribution, we can determine the PDF component by comparing the effective
multifractality of the original time series and the surrogate data that have a
normal distribution and keep the same linear and nonlinear correlations as the
original data. We demonstrate our method by taking the daily volatility data of
Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example.
Extensive numerical experiments show that a time series exhibits effective
multifractality only if it possesses nonlinearity and the PDF has impact on the
effective multifractality only when the time series possesses nonlinearity. Our
method can also be applied to judge the presence of multifractality and
determine its components of multifractal time series in other complex systems.Comment: 9 RevTex pages including 9 eps figures. Comments and suggestions are
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