Increasing market efficiency in the stock markets

We study the temporal evolutions of three stock markets; Standard and Poor's 500 index, Nikkei 225 Stock Average, and the Korea Composite Stock Price Index. We observe that the probability density function of the log-return has a fat tail but the tail index has been increasing continuously in recent years. We have also found that the variance of the autocorrelation function, the scaling exponent of the standard deviation, and the statistical complexity decrease, but that the entropy density increases as time goes over time. We introduce a modified microscopic spin model and simulate the model to confirm such increasing and decreasing tendencies in statistical quantities. These findings indicate that these three stock markets are becoming more efficient. An erratum to this article is available at .     

Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach

ARCH and GARCH stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with Gaussian conditional probability. It can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a Truncated Lévy Flight or GARCH model, but each with individual shortfalls. In this paper therefore, we combine the GARCH process with a conditional truncated Lévy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons.     

Multi-Scale Gaussian Processes： a Novel Model for Chaotic Time Series Prediction

Based on the classical Gaussian process （GP） model, we propose a multi-scale Gaussian process （MGP） model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine. Moreover, the scaling function with its different dilations and translations can form a set of complete bases, resulting in the fact that the MGP can acquire better prediction performance than the GP. The experiments can lead to the following conclusions： （i） The MGP gives a relatively better prediction performance in comparison with the classical GP model. （ii） The prediction performance of the MGP is competitive with support vector machine （SVM）. They give better performance as compared to the radial basis function networks.     

A long-range memory stochastic model of the return in financial markets

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.     

A reflexive toy-model for financial market

We propose a reflexive toy model for market dynamics, based on the idea that existing reflexive loops are generated by the conviction, shared by many market operators, that a certain price follows a certain model. Their trading behaviour will therefore increase the probability that the model predictions are in fact fulfilled. We analytically write the equations generating a reflexive loop stemming from a simple linear regression model, and we show that the resulting toy model yields a peculiar intermittent behavior. The presence of two unstable fixed points is apparent from our numerical calculation and the residence-time distribution density in these points asymptotically follows an inverse-power-law tail. The exponent of this tail, as well as the scaling properties of the model output, are close to those stemming from real-price time series.     

Spread and Quote-Update Frequency of the Limit-Order Driven Sergei Maslov Model

We perform numerical simulations of the limit-order driven Sergei Maslov （SM） model and investigate the probability distribution and autocorrelation function of the bid-ask spread S and the quote-update frequency U. For the probability distribution, the model successfully reproduces the power law decay of the spread and the exponential decay of the quote-update frequency. For the autocorrelation function, both the spread and the quote-update frequency of the model decay by a power law, which is consistent with the empirical study. We obtain the power law exponent 0.54 for the spread, which is in good agreement with the real financial market.     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

What distinguishes individual stocks from the index?

Stochastic volatility models decompose the time series of financial returns into the product of a volatility factor and an iid noise factor. Assuming a slow dynamic for the volatility factor, we show via nonparametric tests that both the index as well as its individual stocks share a common volatility factor. While the noise component is Gaussian for the index, individual stock returns turn out to require a leptokurtic noise. Thus we propose a two-component model for stocks, given by the sum of Gaussian noise, which reflects market-wide fluctuations, and Laplacian noise, which incorporates firm-specific factors such as firm profitability or growth performance, both of which are known to be Laplacian distributed. In the case of purely Gaussian noise, the chi-squared probability for the density of individual stock returns is typically on the order of 10^-20, while it increases to values of O(1) by adding the Laplace component.     

Invariant power law distribution of langevin systems with colored multiplicative noise

The random multiplicative process is studied for the case of a colored multiplicative noise with exponentially decreasing autocorrelation function. We observe the power law exponent of probability distribution in a statistically steady state numerically to clarify the effect of finite correlation time. The renormalization procedure is applied to derive the power law exponent theoretically. The power law exponent is inversely proportional to the autocorrelation time of the multiplicative noise.     

Corrective measures in turbulent pipe flows and extended self-similarity

Significant statistical bias in LDA measurements and how to adequately deal with it is a subtle problem when dealing with turbulent flows. In order to attempt a clarification we have performed measurements on a non-standard “grid experiment” where a clear bias effect is found. We have investigated the effect of several corrective measures and find that best results, in the sense of having the first moment converge to zero, are obtained when using the time between events as statistical weights. The corrected time series have been used to check for extended self-similarity (ESS). Even though no scaling regime is seen for the third moment and the flow certainly is neither isotropic nor homogeneous, perfect ESS scaling based on the absolute third moment is observed up to the twelfth moment, extending into a time domain regime where the Taylor hypothesis of frozen turbulence is obviously violated. Reversing the argument this indicates that the correction scheme needed can be experimentally decided on using the criterion stated above and especially so if ESS is to be expected. Finally we have used the corrected data to quantify the deviations from Gaussian behavior of the velocity difference probability density function for a weakly turbulent flow. Through comparison with results on the Gaussian-Lorentzian distribution we find that the even part of the experimental distribution can be reproduced quite well by a single-parameter family of distributions with second moment equal unity. Received 5 August 1998 and Received in final form 21 December 1998     

Zurek-Kibble mechanism for the spontaneous vortex formation in Nb-Al/Al(ox)/Nb Josephson tunnel junctions: new theory and experiment

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched Nb-Al/Al(ox)/Nb annular Josephson tunnel junctions (JTJs) as a function of the quench time, tau(Q). The probability f(1) to trap a single defect during the normal-metal-superconductor phase transition clearly follows an allometric dependence on tau(Q) with a scaling exponent sigma = 0.5, as predicted from the Zurek-Kibble mechanism for realistic JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealized model was used that predicted sigma = 0.25, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.     

Clustering of volatility as a multiscale phenomenon

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What is well known is that absolute returns have memory on a long time range, this phenomenon is known as clustering of volatility. In this paper we show that volatility correlations are power-laws with a non-unique scaling exponent. This kind of multiscale phenomenology has some analogies with fully developed turbulence and disordered systems and it is now pointed out for financial series. Starting from historical returns series, we have also derived the volatility distribution, and the results are in agreement with a log-normal shape. In our study, we consider the New York Stock Exchange (NYSE), daily composite index closes (January 1966 to June 1998) and the US Dollar/Deutsche Mark (USD-DM) noon buying rates certified by the Federal Reserve Bank of New York (October 1989 to September 1998). Received 1 February 2000     

基于双参数Weibull分布的视频编码率失真模型的研究

对视频序列离散余弦变换(DCT)系数统计分布进行了分析,提出了一种基于Weibull概率密度的视频DCT系数统计模型,该模型较Laplace概率密度与Cauchy概率密度更好地描述了视频序列的DCT特征.随后以该统计模型为基础,依据熵编码的理论分别给出了视频序列的速率-量化关系和失真-量化关系,并根据实际视频序列特性对其进行合理地简化近似,得到一种新的较为精确的视频序列率失真模型.经大量仿真实验证明,文中提出的基于Weibull分布的率失真模型对于Intra帧和Inter帧两种编码的真实视频序列率失真特性都具有较好的描述.     

Are all highly liquid securities within the same class?

In this article 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 Lévy class of stochastic variables.     

滑动移除重标方差在动力学结构突变检验中的应用

标度指数是一个有效的非线性动力学指数,能够针对相关性时间序列动力学结构突变进行检测;通过滑动窗口技术和滑动移除窗口技术,重标极差对于相关时间序列动力学突变具有很好的检测能力,但由于重标极差方法本身的不完善,在滑动移除窗口较小时其检测结果出现一些虚假的突变点和突变区间.鉴于此,本文提出了一种新的动力学检测方法—–滑动移除重标方差.理想序列数值试验表明,滑动移除重标方差具有很强的稳定性和准确性,在滑动窗口较小时其检测结果没有出现虚假的突变点和区间,实测资料的应用进一步验证了新方法的可靠性.     

A universal scaling theory for complexity of analog computation

We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability ensembles of linear programming problems. For each one of these we obtain numerically the probability distribution functions of certain quantities which measure the complexity. Remarkably, in the asymptotic limit of very large problems, each of these probability distribution functions reduces to a universal scaling function, depending on a single scaling variable and independent of the details of its parent probability ensemble. These functions are reminiscent of the scaling functions familiar in the theory of phase transitions. The results reported here extend analytical and numerical results obtained recently for the Gaussian ensemble.     

Power spectral density of self-mixing signals from a flowing Brownian motion system

An analytical expression for the power spectral density of the self-mixing signals from a flowing Brownian motion system irradiated by a focused Gaussian field is derived from the time autocorrelation function of the signals. The power spectral density is composed of two Voigt functions. An improved series summation method (SSM) is proposed to calculate the Voigt function. The characteristics of the power spectral density are analyzed according to the numerical results. The power spectral density can hopefully be used for measuring the flow velocity and the particle size.     

A Markov model of financial returns

We address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long-range correlated second moments. We show that a Markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations. We test the proposed model by analyzing index closing prices of the New York Stock Exchange and the DEM/USD tick-by-tick exchange rates obtained from Reuters EFX. We show that the model captures the characteristic features observed in actual financial time series, including volatility clustering, time scaling and fat tails in the probability density functions, power-law behavior of volatility correlations and, most importantly, the observed nonuniversal multifractal singularity spectrum. Motivated by our finding of strong agreement between the model and the data, we argue that at least two independent stochastic Gaussian variables are required to adequately model price fluctuations.     

Loop dynamics in DNA denaturation

The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.