DCCA cross-correlation coefficient: Quantifying level of cross-correlation

In this paper, a new coefficient is proposed with the objective of quantifying the level of cross-correlation between nonstationary time series. This cross-correlation coefficient is defined in terms of the DFA method and the DCCA method. The implementation of this cross-correlation coefficient will be illustrated with selected time series.     

Study of cross-correlation in a self-affine time series of taxi accidents

We study in this paper the cross-correlation between self-affine time series of real variables recorded simultaneously in cases of taxi accidents. For this purpose, we apply the DCCA method and show that the cross-correlation can be divided into three distinct groups, if we look for the detrended covariance function, i.e., long-range cross-correlations, short-range cross-correlations and no cross-correlations. Finally, it will be seen that the detrended covariance function is robust, if compared with other methods, in identifying these types of cross-correlations.     

DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity

In this paper we propose, analyze and also quantify cross-correlations between climatological data. For this purpose we adopt the DCCA cross-correlation coefficient ρ_DCCA. In order to accomplish this goal, we calculate the cross-correlation between time series of air temperature and relative humidity. This analysis was performed taking into account several stations (cities) around the world. The results found here, depending on the station location, may exhibit one of the following behaviors, i.e., negative, positive, or null cross-correlations. It is noteworthy that, the level of cross-correlation between air temperature and relative humidity is quantified in these cases. Finally, DCCA cross-correlation coefficients show that, in general, the data are influenced by seasonal components.     

Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.     

Price–volume cross-correlation analysis of CSI300 index futures

We investigate the cross-correlation between price returns and trading volumes for the China Securities Index 300 (CSI300) index futures, which are the only stock index futures traded on the China Financial Futures Exchange (CFFEX). The basic statistics suggest that distributions of these two time series are not normal but exhibit fat tails. Based on the detrended cross-correlation analysis (DCCA), we obtain that returns and trading volumes are long-range cross-correlated. The existence of multifractality in the cross-correlation between returns and trading volumes has been proven with the multifractal detrended cross-correlation analysis (MFDCCA) algorithm. The multifractal analysis also confirms that returns and trading volumes have different degrees of multifractality. We further perform a cross-correlation statistic to verify whether the cross-correlation significantly exists between returns and trading volumes for CSI300 index futures. In addition, results of the test for lead-lag effect demonstrate that contemporaneous cross-correlation of return and trading volume series is stronger than cross-correlations of leaded or lagged series.     

Detrended cross-correlation analysis of electroencephalogram

In the paper we use detrended cross-correlation analysis (DCCA) to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject's brain function is healthy or not.     

Statistical appearance of nonuniform fluctuations in a wide-gap n-n-n-n device

A cross-correlation matrix applied for restoring the doping profile in an n⁺-n⁻-n-n⁺ device was reported recently [Y.-H. Shiau, Solid-State Electron. 50 (2006) 191]. In this paper we will show that this statistical method is very useful for detecting the dynamical processes embedded in semiconductor devices. In addition, extraction of nonuniform fluctuations hidden in this wide-gap semiconductor device could be helpful for clarifying the previous studies on several competing instabilities in InSb at 77 K [A. ?enys, G. Lasiene, K. Pyragas, Solid-State Electron. 35 (1992) 975; H. Ito, Y. Ueda, Phys. Lett. A 280 (2001) 312]. A general discussion about the application of the cross-correlation matrix to other pattern-forming systems is also given in the present study.     

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, , is λ=1.17±0.04 which is almost similar for all underlying rivers at 1σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ∈(0.76,0.85) and γ_×∈(0.30,0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), is confirmed.     

Structure of a financial cross-correlation matrix under attack

We investigate the structure of a perturbed stock market in terms of correlation matrices. For the purpose of perturbing a stock market, two distinct methods are used, namely local and global perturbation. The former involves replacing a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series while the latter reconstructs the cross-correlation matrix just after replacing the original return series with Gaussian-distributed time series. Concerning the local case, it is a technical study only and there is no attempt to model reality. The term ‘global’ means the overall effect of the replacement on other untouched returns. Through statistical analyses such as random matrix theory (RMT), network theory, and the correlation coefficient distributions, we show that the global structure of a stock market is vulnerable to perturbation. However, apart from in the analysis of inverse participation ratios (IPRs), the vulnerability becomes dull under a small-scale perturbation. This means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small-scale perturbation. In contrast, when going down to the structure of business sectors, we confirm that correlation-based business sectors are regrouped in terms of IPRs. This result gives a clue about monitoring the effect of hidden intentions, which are revealed via portfolios taken mostly by large investors.     

小管径气液两相流空隙率波传播的多尺度相关性

空隙率波是气液两相流系统的特殊物理现象,理解空隙率波的传播特性对揭示两相流流型转变与流速测量物理机理具有重要意义.本文首先考察了典型非线性系统的多尺度互相关特性,发现去趋势互相关分析方法可有效揭示系统的多尺度非线性动力学特征;然后,通过采集垂直上升小管径气液两相流电导传感器阵列上下游空隙率波动数据,提出采用多尺度去趋势互相关分析方法探测空隙率波传播的多尺度互相关特性,并提取了低尺度空隙率波互相关水平增长率;另外,通过计算空隙率波空间衰减因子,考察了气液两相流空隙率波传播的结构不稳定行为.结果表明,空隙率波结构的多尺度互相关特性与其空间衰减特性具有较好的物理关联性:对于气液两相流过渡流型,低尺度空隙率波互相关水平增长率较高,且与较为稳定的空隙率波传播特性相对应;而当气液两相流空隙率波明显衰减或放大时,空隙率波互相关水平增长速率一般较低.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Parameter estimation using balanced synchronization

Synchronization between experimental observations and a dynamical model with undetermined parameters can assist in completing the specification of the model parameters. The quality of the synchronization, a cost function to be minimized, typically depends on the difference between the data time series and the model time series. If the coupling between the data and the model is too strong, this cost function is small for any data and any model, and the variation of the cost function with respect to the parameters of interest is too small to permit selection of a value of the parameters. If the coupling is too small, synchronization is lost. We introduce two methods for balancing the competing desires of a small cost function and the numerical ability to determine parameters accurately. One method of ‘balanced’ synchronization adds a requirement that the conditional Lyapunov exponent of the model system, conditioned on being driven by the data, remain negative but small. The other method allows the coupling to vary in time according to the error in synchronization. This second method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined.     

Regime switching dynamics in credit default swaps: Evidence from smooth transition autoregressive model

This paper investigates the dynamics of credit default swap (CDS) spread. We first find auto-correlations and cross-correlations of the CDS series and the CDS average by employing detrended cross-correlation analysis (DCCA). We then employ smooth transition autoregressive (STAR) models to characterize the regime switching behavior of 28 US corporate CDS series from January 2007 through October 2009. In each case, we find clear evidence for transitions between low-price and high-price regimes. The threshold estimations of the STAR model effectively differentiate the price regimes, where the first transition consistently coincides with the explosion of the crisis in late 2008.     

Synchronization analysis of delayed complex networks with time-varying couplings

In this paper, a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays. The coupling configurations are not restricted to the symmetric and irreducible connections or the non-negative off-diagonal links. The stability criteria are obtained by using Lyapunov-Krasovskii functional method and subspace projection method. These criteria reveal the relationship between coupling matrices and stability of the dynamical networks.     

Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multifractal detrended fluctuation analysis (MF-DFA) method and is quite accurate for small size data sets. As compared to polynomial fits in the MF-DFA, a single Daubechies wavelet is used here for detrending purposes. The natural, built-in variable window size in wavelet transforms makes this procedure well suited for non-stationary data. We illustrate the working of this method through the analysis of binomial multifractal model. For this model, our results compare well with those calculated analytically and obtained numerically through MF-DFA. To show the efficacy of this approach for finite data sets, we also do the above comparison for Gaussian white noise time series of different sizes. In addition, we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2D Ising model.     

Globalization — Entropy unification through the Theil index

A time series is remapped onto an entropy concept, based on the Theil index. The Manhattan distance between these surrogate series is calculated, and contrasted to the usual correlation distance measure. The idea is applied to several Gross Domestic Product (relative increments) of rich countries. Such distances are calculated for various time window sizes. The role of time averaging in such finite size windows is discussed. We construct the locally minimum spanning tree (LMST) corresponding to the distance matrix. Another hierarchical network structure (Unidirectional Minimal Length Path) is compared with the LMST for confirming that the mean distance between the most developed countries on different networks actually decreases in time, — which we consider as a proof of economy globalization. It is stressed that this entropy distance measure seems more suitable in detecting some “phase transition” in time series, like a globalization process than the usual correlation based measure.     

Pattern interdependent network of cross-correlation in multivariate time series

Cross-correlation of a bivariate time series induces interdependencies between local patterns in the two series, which cooperatively exhibit in turn the structure of the cross-correlation. However, this structure is lost in the procedure of statistical average in time series analysis. In this paper a new concept called pattern interdependent network is proposed to display the structure of cross-correlation, in which the nodes are unique local patterns and the linkages are co-occurring frequencies of the unique local patterns in the series. The performance is illustrated by the bivariate series generated with the Gaussian process and the auto-regressive fractionally integrated moving average (ARFIMA) model. It is found that the cross-correlation and the scaling behaviors dominate the pattern of backbone structure (the set of the nodes and the set of linkages) and the symmetry of the network, respectively. The ARFIMA model can reproduce the structural behaviors of cross-correlations in U.S. stock markets. This concept provides us with a new method for detecting the structure of couplings between time series in various fields, such as clinical pathological signals.     

A novel study of parity and attractor in the time reversed Lorentz system

In this Letter, a new effective approach to achieve adaptive synchronization is proposed. Via using Ge-Yao-Chen (GYC) partial region stability theory and pragmatical asymptotically stability theorem, the numerical simulation results show that the states errors and parameter errors approach to zero much more exactly and efficiently than traditional method. The time reversed Lorenz system (called historical Lorenz system in this Letter) is introduced and used for example in this Letter. The simulation results are given in figures and tables for comparison between the new approach and traditional one to show the effectiveness and feasibility of our new strategy.     

Correlation measure to detect time series distances, whence economy globalization

An instantaneous time series distance is defined through the equal time correlation coefficient. The idea is applied to the Gross Domestic Product (GDP) yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation. Some data discussion is first presented to decide what (EKS, GK, or derived) GDP series should be studied. Distances are then calculated from the correlation coefficient values between pairs of series. The role of time averaging of the distances over finite size windows is discussed. Three network structures are next constructed based on the hierarchy of distances. It is shown that the mean distance between the most developed countries on several networks actually decreases in time, —which we consider as a proof of globalization. An empirical law is found for the evolution after 1990, similar to that found in flux creep. The optimal observation time window size is found ?15 years.