Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets

Statistical studies that consider multiscale relationships among several variables use wavelet correlations and cross-correlations between pairs of variables. This procedure needs to calculate and compare a large number of wavelet statistics. The analysis can then be rather confusing and even frustrating since it may fail to indicate clearly the multiscale overall relationship that might exist among the variables. This paper presents two new statistical tools that help to determine the overall correlation for the whole multivariate set on a scale-by-scale basis. This is illustrated in the analysis of a multivariate set of daily Eurozone stock market returns during a recent period. Wavelet multiple correlation analysis reveals the existence of a nearly exact linear relationship for periods longer than the year, which can be interpreted as perfect integration of these Euro stock markets at the longest time scales. It also shows that small inconsistencies between Euro markets seem to be just short within-year discrepancies possibly due to the interaction of different agents with different trading horizons.     

A quantum statistical approach to simplified stock markets

We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the portfolio of a certain trader to a different one. This computation can also be carried out using some kind of Feynman graphs adapted to the present context.     

The Forbes 400, the Pareto power-law and efficient markets

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.     

A new perturbation method to the Tent map and its application

Disturbance imposed on the chaotic systems is an effective way to maintain its chaotic good encryption features. This paper proposes a new perturbation method to the Tent map. First it divides the Tent map domain into 2^N parts evenly and selects a particular part from them, then proliferates the Tent map mapping trajectory of this particular part, which can disturb the entire system disturbance. The mathematical analysis and simulated experimental results prove that the disturbed Tent map has uniform invariant distribution and can produce good cryptographic properties of pseudo-random sequence. These facts avoid the phenomenon of short-period caused by the computer's finite precision and reducing the sequence's dependence on the disturbance signal, such that effectively compensate for the digital chaotic system dynamics degradation.     

Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices

A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes. Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S=1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S=1/2, the computational results of CMC are incomparable to those predicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature. The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to ±1/2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems.     

一种基于自相关函数的幂律检测器

针对水下高斯噪声中非高斯瞬态信号的检测问题,在研究Nuttall提出的power-law(幂律)检测器的基础上,为了提高其检测性能,依据信号和噪声的自相关函数的差异,提出了基于自相关函数的power-law检测器,并对其参数的最佳选取及检测性能进行了仿真研究。仿真结果表明,基于自相关函数的检测器较基于DFT的power-law检测器性能有所提高,有一定的可行性。     

A new auxiliary equation method and its application to the Sharma-Tasso-Olver model

A new auxiliary equation method, constructed by a first order nonlinear ordinary differential equation with at most an eighth-degree nonlinear term, is first proposed for exploring more exact solutions to nonlinear evolution equations. Being concise and straightforward, the method, with the aid of symbolic computation, is applied to the Sharma-Tasso-Olver model, and some new exact solitary wave solutions are obtained. The approach is also applicable to searches for exact solutions of other nonlinear evolution equations.     

Cross-correlations between agricultural commodity futures markets in the US and China

This paper examines the cross-correlation properties of agricultural futures markets between the US and China using a cross-correlation statistic test and multifractal detrended cross-correlation analysis (MF-DCCA). The results show that the cross-correlations between the two geographically distant markets for four pairs of important agricultural commodities futures are significantly multifractal. By introducing the concept of a “crossover”, we find that the multifractality of cross-correlations between the two markets is not long lasting. The cross-correlations in the short term are more strongly multifractal, but they are weakly so in the long term. Moreover, cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term while cross-correlations of all kinds of fluctuations for soy bean and soy meal futures are persistent and for corn and wheat futures are anti-persistent in the long term. We also find that cross-correlation exponents are less than the averaged generalized Hurst exponent when q<0$q<0$ and more than the averaged generalized Hurst exponent when q>0$q>0$ in the short term, while in the long term they are almost the same.     

A quantile-based Time at Risk: A new approach for assessing risk in financial markets

In this paper, we provide a new measure for evaluation of risk in financial markets. This measure is based on the return interval of critical events in financial markets or other investment situations. Our main goal was to devise a model like Value at Risk (VaR). As VaR, for a given financial asset, probability level and time horizon, gives a critical value such that the likelihood of loss on the asset over the time horizon exceeds this value is equal to the given probability level, our concept of Time at Risk (TaR), using a probability distribution function of return intervals, provides a critical time such that the probability that the return interval of a critical event exceeds this time equals the given probability level. As an empirical application, we applied our model to data from the Tehran Stock Exchange Price Index (TEPIX) as a financial asset (market portfolio) and reported the results.     

A time-series approach to measuring node similarity in networks and its application to community detection

A central concept in network analysis is that of similarity between nodes. In this paper, we introduce a dynamic time-series approach to quantifying the similarity between nodes in networks. The problem of measuring node similarity is exquisitely embedded into the framework of time series for state evolution of nodes. We develop a deterministic parameter-free diffusion model to drive the dynamic evolution of node states, and produce a unique time series for each source node. Then we introduce a measure quantifying how far all the other nodes are located from each source one. Following this measure, a quantity called dissimilarity index is proposed to signify the extent of similarity between nodes. Thereof, our dissimilarity index gives a deep and natural integration between the local and global perspectives of topological structure of networks. Furthermore, we apply our dissimilarity index to unveil community structure in networks, which verifies the proposed dissimilarity index.     

Complexity-entropy causality plane: A useful approach to quantify the stock market inefficiency

The complexity-entropy causality plane has been recently introduced as a powerful tool for discriminating Gaussian from non-Gaussian process and different degrees of correlations [O.A. Rosso, H.A. Larrondo, M.T. Martín, A. Plastino, M.A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett. 99 (2007) 154102]. We propose to use this representation space to distinguish the stage of stock market development. Our empirical results demonstrate that this statistical physics approach is useful, allowing a more refined classification of stock market dynamics.     

Conditional independence graph for nonlinear time series and its application to international financial markets

Conditional independence graphs are proposed for describing the dependence structure of multivariate nonlinear time series, which extend the graphical modeling approach based on partial correlation. The vertexes represent the components of a multivariate time series and edges denote direct dependence between corresponding series. The conditional independence relations between component series are tested efficiently and consistently using conditional mutual information statistics and a bootstrap procedure. Furthermore, a method combining information theory with surrogate data is applied to test the linearity of the conditional dependence. The efficiency of the methods is approved through simulation time series with different linear and nonlinear dependence relations. Finally, we show how the method can be applied to international financial markets to investigate the nonlinear independence structure.     

A new kind of special function and its application

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented.     

Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets

In this paper, we investigate the cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong. We use not only the qualitative analysis of the cross-correlation test, but also the quantitative analysis of the MF-X-DFA. Our findings confirm the existence of cross-correlations between the stock market in China and markets in Japan, South Korea and Hong Kong, which have strongly multifractal features. We find that the cross-correlations display the characteristic of multifractality in the short term. Moreover, the cross-correlations of small fluctuations are persistent and those of large fluctuations are anti-persistent in the short term, while the cross-correlations of all kinds of fluctuations are persistent in the long term. Furthermore, based on the multifractal spectrum, we also find that the multifractality of cross-correlation between stock markets in China and Japan are stronger than those between China and South Korea, as well as between China and Hong Kong.     

An axiomatic approach to the number operator and its application to parastatistics

An axiomatic approach to the number operator based on four physically motivated axioms is developed. A connection between the number operator and some generators on representations of group of all unitary transformations of Hilbert space is shown. In consequence, a new generalization of statistics is clarified. In the finite-dimensional case an example of noncommuting number operator is given.     

A new approach to peratization technique

The usual method of peratization technique is to expand scattering lengthA(a) in Born series in powers of the coupling constantg. In this paper a new approach to the peratization technique has been discussed starting with the standard equation for the scattering length. As an application of the theory developed, the cases of inverse fourth power and a logarithmic singular potentials have been discussed.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

A new approach to Burger's equation

A new approach to Burger's equation is proposed using the decomposition method, eliminating smallness assumptions or linearization.