共查询到20条相似文献,搜索用时 52 毫秒
1.
F. Wang P. Weber K. Yamasaki S. Havlin H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(2):123-133
We discuss recent results concerning statistical regularities in the
return intervals of volatility in financial markets. In particular, we
show how the analysis of volatility return intervals, defined as the
time between two volatilities larger than a given threshold, can help
to get a better understanding of the behavior of financial time
series. We find scaling in the distribution of return intervals for
thresholds ranging over a factor of 25, from 0.6 to 15 standard
deviations, and also for various time windows from one minute up to
390 min (an entire trading day). Moreover, these results are
universal for different stocks, commodities, interest rates as well as
currencies. We also analyze the memory in the return intervals which
relates to the memory in the volatility and find two scaling regimes,
ℓ<ℓ* with α1=0.64±0.02 and ℓ> ℓ*
with α2=0.92±0.04; these exponent values are similar to
results of Liu et al. for the volatility. As an application, we use
the scaling and memory properties of the return intervals to suggest a
possibly useful method for estimating risk. 相似文献
2.
I. Vodenska-Chitkushev F. Z. Wang P. Weber K. Yamasaki S. Havlin H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,61(2):217-223
We analyze the S&P 500 index data for the 13-year period, from
January 1, 1984 to December 31, 1996, with one data point every 10
min. For this database, we study the distribution and clustering
of volatility return intervals, which are defined as the time
intervals between successive volatilities above a certain threshold
q. We find that the long memory in the volatility leads to a
clustering of above-median as well as below-median return intervals.
In addition, it turns out that the short return intervals form
larger clusters compared to the long return intervals. When
comparing the empirical results to the ARMA-FIGARCH and fBm models
for volatility, we find that the fBm model predicts scaling better
than the ARMA-FIGARCH model, which is consistent with the argument
that both ARMA-FIGARCH and fBm capture the long-term dependence in
return intervals to a certain extent, but only fBm accounts for the
scaling. We perform the Student's t-test to compare the empirical
data with the shuffled records, ARMA-FIGARCH and fBm. We analyze
separately the clusters of above-median return intervals and the
clusters of below-median return intervals for different thresholds
q. We find that the empirical data are statistically different
from the shuffled data for all thresholds q. Our results also
suggest that the ARMA-FIGARCH model is statistically different from
the S&P 500 for intermediate q for both above-median and
below-median clusters, while fBm is statistically different from
S&P 500 for small and large q for above-median clusters and for
small q for below-median clusters. Neither model can fully explain
the entire regime of q studied. 相似文献
3.
S. C. Wang J. J. Tseng C. C. Tai K. H. Lai W. S. Wu S. H. Chen S. P. Li 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(1):105-111
Many systems of different nature exhibit scale free behaviors. Economic
systems with power law distribution in the wealth are one of the examples.
To better understand the working behind the complexity, we undertook an
experiment recording the interactions between market participants.
A Web server was setup to administer the exchange of
futures contracts whose liquidation prices were coupled to event outcomes.
After free registration, participants started trading to compete for
the money prizes upon maturity of the futures contracts at the end of
the experiment. The evolving `cash' flow
network was reconstructed from the transactions between players.
We show that the network topology is hierarchical, disassortative and
small-world with a power law exponent of
1.02±0.09 in the degree distribution after an exponential decay correction.
The small-world property emerged early in the experiment while the number
of participants was still small.
We also show power law-like distributions of the net incomes and
inter-transaction time intervals. Big winners and losers are associated with
high degree, high betweenness centrality,
low clustering coefficient and low degree-correlation. We identify communities
in the network as groups of the like-minded. The distribution of the
community sizes is shown to be power-law distributed with an exponent of
1.19±0.16. 相似文献
4.
Z.-Q. Jiang L. Guo W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):347-355
A phenomenological investigation of the endogenous and
exogenous dynamics in the fluctuations of capital fluxes is carried
out on the Chinese stock market using mean-variance analysis,
fluctuation analysis, and their generalizations to higher orders.
Non-universal dynamics have been found not only in the scaling
exponent α, which is different from the universal values 1/2
and 1, but also in the distributions of the ratio η=
σexo / σendo of individual stocks. Both
the scaling exponent α of fluctuations and the Hurst exponent
Hi increase in logarithmic form with the time scale Δt
and the mean traded value per minute 〈fi 〉,
respectively. We find that the scaling exponent αendo
of the endogenous fluctuations is independent of the time scale.
Multiscaling and multifractal features are observed in the data as
well. However, the inhomogeneous impact model is not verified. 相似文献
5.
R. Kitt J. Kalda 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):141-145
The question of optimal portfolio is addressed. The conventional Markowitz portfolio optimisation is discussed and the shortcomings
due to non-Gaussian security returns are outlined.
A method is proposed to minimise the likelihood of extreme non-Gaussian drawdowns of the portfolio value.
The theory is called Leptokurtic, because it minimises the effects from “fat tails” of returns. The leptokurtic portfolio
theory provides an optimal portfolio for investors, who define their risk-aversion as unwillingness to experience sharp drawdowns
in asset prices. Two types of risks in asset returns are defined: a fluctuation risk, that has Gaussian distribution, and
a drawdown risk, that deals with distribution tails. These risks are quantitatively measured by defining the “noise kernel”
— an ellipsoidal cloud of points in the space of asset returns.
The size of the ellipse is controlled with the threshold parameter: the larger the threshold parameter, the larger return
are accepted for investors as normal fluctuations.
The return vectors falling into the kernel are used for calculation of fluctuation risk. Analogously, the data points falling
outside the kernel are used for the calculation of drawdown risks. As a result the portfolio optimisation problem becomes
three-dimensional: in addition to the return, there are two types of risks involved. Optimal portfolio for drawdown-averse
investors is the portfolio minimising variance outside the noise kernel. The theory has been tested with MSCI North America,
Europe and Pacific total return stock indices. 相似文献
6.
O. S. Klass O. Biham M. Levy O. Malcai S. Solomon 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(2):143-147
Statistical regularities at
the top end of the wealth distribution in the United States are
examined using the Forbes 400 lists of richest Americans,
published between 1988 and 2003.
It is found that the wealths are distributed according to a power-law
(Pareto) distribution.
This result is explained using a
simple stochastic model
of multiple investors that incorporates the
efficient market hypothesis
as well as the multiplicative nature of financial market fluctuations. 相似文献
7.
I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility
function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed
power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power
law is a power law heterogeneity of traders' investment time horizons. 相似文献
8.
W. Q. Duan 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(2):271-276
Identifying universal patterns in complex economic
systems can reveal the dynamics and organizing principles underlying the
process of system evolution. We investigate the scaling behaviours that have
emerged in the international trade system by describing them as a series of
evolving weighted trade networks. The maximum-flow spanning trees (constructed by maximizing the total
weight of the edges) of these networks exhibit two universal scaling
exponents: (1) topological scaling exponent η = 1.30 and (2) flow
scaling exponent ζ = 1.03. 相似文献
9.
M. Bartolozzi C. Mellen T. Di Matteo T. Aste 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(2):207-220
In the present work we investigate the multiscale nature of the
correlations for high frequency data (1 min) in different
futures markets over a period of two years, starting on the
1st of January 2003 and ending on the 31st of
December 2004. In particular, by using the concept of local
Hurst exponent, we point out how the behaviour of this parameter,
usually considered as a benchmark for persistency/antipersistency
recognition in time series, is largely time-scale dependent in the
market context. These findings are a direct consequence of the
intrinsic complexity of a system where trading strategies are
scale-adaptive. Moreover, our analysis points out different
regimes in the dynamical behaviour of the market indices under
consideration. 相似文献
10.
R. N. Onody G. M. Favaro E. R. Cazaroto 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(4):487-493
The GARCH (p, q) model is a very interesting stochastic process with
widespread applications and a central role in empirical finance. The
Markovian GARCH (1, 1) model has only 3 control parameters and a
much discussed question is how to estimate them when a series of
some financial asset is given. Besides the maximum likelihood
estimator technique, there is another method which uses the
variance, the kurtosis and the autocorrelation time to determine
them. We propose here to use the standardized 6th moment. The set
of parameters obtained in this way produces a very good probability
density function and a much better time autocorrelation function.
This is true for both studied indexes: NYSE Composite and FTSE 100.
The probability of return to the origin is investigated at different
time horizons for both Gaussian and Laplacian GARCH models. In spite
of the fact that these models show almost identical performances
with respect to the final probability density function and to the
time autocorrelation function, their scaling properties are,
however, very different. The Laplacian GARCH model gives a better
scaling exponent for the NYSE time series, whereas the Gaussian
dynamics fits better the FTSE scaling exponent. 相似文献
11.
We perform return interval analysis of 1-min realized volatility defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated. In comparison with the volatility defined by the closest tick prices to the minute marks, the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks (out of 22 stocks) and the SSEC pass the Kolmogorov-Smirnov (KS) test and exhibit scaling behaviors, among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the KS goodness-of-fit test under the significance level of 5%. The improved scaling behavior is further confirmed by the relation between the fitted exponent γ and the threshold q. In addition, the similarity of the return interval distributions for different stocks is also observed for the realized volatility. The investigation of the conditional probability distribution and the detrended fluctuation analysis (DFA) show that both short-term and long-term memory exists in the return intervals of realized volatility. 相似文献
12.
The statistical properties of the return intervals τq between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τq for different thresholds q. Furthermore, the KS test and weighted KS test show that the scaled return interval distributions of 6 stocks (out of the 12 stocks) can be nicely fitted by a stretched exponential function with γ≈0.31 under the significance level of 5%, where is the mean return interval. The investigation of the conditional probability distribution Pq(τ|τ0) and the mean conditional return interval 〈τ|τ0〉 demonstrates the existence of short-term correlation between successive return interval intervals. We further study the mean return interval 〈τ|τ0〉 after a cluster of n intervals and the fluctuation F(l) using detrended fluctuation analysis, and find that long-term memory also exists in the volatility return intervals. 相似文献
13.
G.-F. Gu W. Chen W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(1):81-87
The statistical properties of the bid-ask spread of a
frequently traded Chinese stock listed on the Shenzhen Stock
Exchange are investigated using the limit-order book data. Three
different definitions of spread are considered based on the time
right before transactions, the time whenever the highest buying
price or the lowest selling price changes, and a fixed time
interval. The results are qualitatively similar no matter linear
prices or logarithmic prices are used. The average spread exhibits
evident intraday patterns consisting of a big L-shape in morning
transactions and a small L-shape in the afternoon. The distributions
of the spread with different definitions decay as power laws. The
tail exponents of spreads at transaction level are well within the
interval (2,3) and that of average spreads are well in line with
the inverse cubic law for different time intervals. Based on the
detrended fluctuation analysis, we found the evidence of long memory
in the bid-ask spread time series for all three definitions, even
after the removal of the intraday pattern. Using the classical
box-counting approach for multifractal analysis, we show that the
time series of bid-ask spread do not possess multifractal nature. 相似文献
14.
Z. Eisler J. Kertész 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(1):145-154
We reanalyze high resolution data from the New York Stock
Exchange and find a monotonic (but not power law) variation of the mean value per trade,
the mean number of trades per minute and the mean trading activity
with company capitalization. We show that the second moment of the
traded value distribution is finite. Consequently, the Hurst
exponents for the corresponding time series can be calculated. These
are, however, non-universal: The persistence grows with larger
capitalization and this results in a logarithmically increasing Hurst exponent. A similar
trend is displayed by intertrade time intervals.
Finally, we demonstrate that the distribution of the intertrade times is
better described by a multiscaling ansatz than by simple gap scaling. 相似文献
15.
T. S. Evans 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):65-69
Evolving networks with a constant number of edges may be
modelled using a rewiring process. These models are used to
describe many real-world processes including the evolution of
cultural artifacts such as family names, the evolution of gene
variations, and the popularity of strategies in simple
econophysics models such as the minority game. The model is
closely related to Urn models used for glasses, quantum gravity
and wealth distributions. The full mean field equation for the
degree distribution is found and its exact solution and generating
solution are given. 相似文献
16.
G.-H. Mu W. Chen J. Kertész W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(1):145-152
The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese
stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks
exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the
“q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at
different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for
multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes.
Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α>
2, well outside the Lévy regime. 相似文献
17.
S. Drożdż A. Z. Górski J. Kwapień 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(4):499-502
World currency network constitutes one of the most complex structures that
is associated with the contemporary civilization. On a way towards
quantifying its characteristics we study the
cross correlations in changes of the daily foreign exchange rates within
the basket of 60 currencies in the period December 1998–May 2005. Such
a dynamics turns out to predominantly involve one outstanding eigenvalue
of the correlation matrix. The magnitude of this eigenvalue depends however
crucially on which currency is used as a base currency for the remaining ones.
Most prominent it looks from the perspective of a peripheral currency.
This largest eigenvalue is seen to systematically decrease and thus
the structure of correlations becomes more heterogeneous,
when more significant currencies are used as reference.
An extreme case in this later respect is the USD in the period considered.
Besides providing further insight into subtle nature of complexity,
these observations point to a formal procedure that in general
can be used for practical purposes of measuring the relative
currencies significance on various time horizons. 相似文献
18.
T. Kaizoji 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):123-127
In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention
on the relative price defined as X(t) = S(t)/S(0), where S(0), is the stock price for an onset time of the bubble. We selected
approximately 3200 stocks traded on the Japanese Stock Exchange, and formed a statistical ensemble of daily relative prices
for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period in which
internet Bubble formed and crashed in the Japanese stock market.
We found that the upper tail of the complementary cumulative distribution function of the ensemble of the relative prices
in the high value of the price is well described by a power-law distribution, P(S>x) ∼x-α , with an exponent that moves over time. Furthermore we found that as the power-law exponents α approached two, the bubble burst. It is reasonable to suppose that it indicates that internet bubble is about to burst. 相似文献
19.
We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution Pq(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution Pq(τ|τ0), the mean conditional interval 〈τ|τ0〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P±(t) and find that P−(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets. 相似文献
20.
J.-P. Bouchaud L. Laloux M. A. Miceli M. Potters 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,55(2):201-207
We present a general method to detect and extract
from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality.
Our central result is derived from the theory of free random matrices, and gives an explicit expression for the interval where
singular values are expected in the absence of any true correlations between the variables under study. Our result can be
seen as the natural generalization of the Marčenko-Pastur distribution for the case of rectangular correlation matrices. We
illustrate the interest of our method on a set of macroeconomic time series. 相似文献