Using Detrended Cross-Correlation Analysis in geophysical data

Detrended cross correlation analysis (DCCA) is used to identify and characterize correlated data obtained in drilled oil wells. The investigation is focused on different petro-physical measurements within the same well, and of the same measurement from two wells in the same oil field. The evaluation of cross correlation exponents indicates if scaling properties in two measurements are alike. The work considers also the values of cross correlated coefficients, which provide an assessment on the local correlation between measurements. The existence of several highly correlated events provides information on the continuity of geological structures, including partial and global dislocations of deposited layers.     

Analysis of signal fluctuations of Cortical Spreading Depression: Preliminary findings

In this work, we apply Detrended Fluctuation Analysis (DFA) to study the dynamics of electrical cortical activity in rats during the phenomenon of Cortical Spreading Depression (CSD), as well as the periods before and after this phenomenon. The characteristic of CSD is reduced electrical activity that occurs and spreads in the cerebral cortex after the application of electrical, chemical or mechanical stimulus. Our results show that the electrocorticogram signal shows long range temporal correlations and scaling behavior, except during the pre-CSD burst phase (significant increase of amplitude provoked by stimulus).     

Memory effect and multifractality of cross-correlations in financial markets

We introduce an instantaneous and an average instantaneous cross-correlation function to detect the temporal cross-correlations between individual stocks based on the daily data of the United States and the Chinese stock markets. The memory effect of the instantaneous cross-correlations is investigated by applying the detrended fluctuation analysis (DFA), where the DFA exponents can be partly explained by the correlation function from the common sense. Long-range memory is observed for the average instantaneous cross-correlations, and persists up to a month magnitude of timescale for the United States stock market and half a month magnitude of timescale for the Chinese stock market. In addition, multifractal nature is investigated by a multifractal detrended fluctuation analysis.     

Nonlinear bivariate dependency of price-volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis

Nonlinear dependency between characteristic financial and commodity market quantities (variables) is crucially important, especially between trading volume and market price. Studies on nonlinear dependency between price and volume can provide practical insights into market trading characteristics, as well as the theoretical understanding of market dynamics. Actually, nonlinear dependency and its underlying dynamical mechanisms between price and volume can help researchers and technical analysts in understanding the market dynamics by integrating the market variables, instead of investigating them in the current literature. Therefore, for investigating nonlinear dependency of price-volume relationships in agricultural commodity futures markets in China and the US, we perform a new statistical test to detect cross-correlations and apply a new methodology called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), which is an efficient algorithm to analyze two spatially or temporally correlated time series. We discuss theoretically the relationship between the bivariate cross-correlation exponent and the generalized Hurst exponents for time series of respective variables. We also perform an empirical study and find that there exists a power-law cross-correlation between them, and that multifractal features are significant in all the analyzed agricultural commodity futures markets.     

Assessment of long-range correlation in animal behavior time series: The temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Detrended Fluctuation Analysis (DFA) is a method that has been frequently used to determine the presence of long-range correlations in human and animal behaviors. However, according to previous authors using statistical model systems, in order to correctly use DFA different aspects should be taken into account such as: (1) the establishment by hypothesis testing of the absence of short term correlation, (2) an accurate estimation of a straight line in the log–log plot of the fluctuation function, (3) the elimination of artificial crossovers in the fluctuation function, and (4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus  ). In our study, modeling the data with the general autoregressive integrated moving average (ARFIMA) model, we rejected the hypothesis of short-range correlations (d=0)$(d=0)$ in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations.     

Limb dominance changes in walking evolution explored by asymmetric correlations in gait dynamics

Fluctuations in the stride interval time series of unconstrained walking are not random but seem to exhibit long-range correlations that decay as a power law (Hausdorff et al. (1995) [35]). Here, we examine whether asymmetries are present in the long-range correlations of different gait parameters (stride, swing and stance intervals) for the left and right limbs. Gait dynamics corresponding to 16 healthy subjects were obtained from the Physionet database, which contains stride, stance and swing intervals for both left and right limbs. Detrended Fluctuation Analysis (DFA) revealed the presence of asymmetric long-range correlations in all gait cycle variables investigated. A rich variety of scaling exponent dynamics was found, with the presence of synchronicity, decreased correlations and dominant correlations. The results are discussed in terms of the hypothesis that reduced strength of long-range correlations reflect both enhanced stability and adaptability.     

Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data

This work is devoted to the study of long correlations, memory effects and other statistical properties of high frequency (tick) data. We use a sample of 25 stocks for this purpose.We verify that the behavior of the return is compatible with that of continuous time Levy processes. We also study the presence of memory effects and long-range correlations in the values of the return.     

Dynamical mechanism of two-phase phenomena in financial markets

Two-phase behavior of the Korean treasury bond (KTB) futures in the Korean exchange market is investigated in this study. To show that the two-phase phenomena are due to heavy-tailed behavior of distribution of price returns, actual data from the KTB futures market with shuffled data and a generated time series are examined according to the Brownian process. In addition, we study the correlation inherent in the KTB futures and its Brownian walk, describing the extent to which the volatility clustering plays a crucial role in equilibrium and nonequilibrium states of financial markets. It is shown that the two-phase behavior essentially results from heavy-tailed behavior of the distribution of price returns. This two-phase behavior does not appear to be relevant to volatility clustering.     

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.     

互相关分析在近红外光谱预处理中的应用

采用互相关分析的光谱预处理方法与一元线性回归结合 ,利用近红外光谱法定量检测了苯和甲苯混合物溶液中苯的体积百分比含量 ;从理论和实验两个方面证明了在一定的条件下经过互相关变换后的光谱信号与目标物质浓度含量呈正比例关系 ,利用这个正比例关系建立一元线性回归方程可以定量检测混合物中目标物质的含量。并且深入探讨了互相关分析作为一种近红外光谱预测量方法的优缺点     

Auto- and cross-correlations in the spinful topological Kondo model

The correlations in charge transport in multiple Majorana fermions systems contain much richer physics and carry more information than the conventional transport coefficients. We calculate the auto- and cross-correlations in the spinful topological Kondo model (SKTM) and point out the frequencies dependencies of the correlations that may serve as a proof of the existence of the Majorana fermions in our system, particularly the change of the cross-correlation from positive to negative at higher frequency.     

Multifractal detrended cross-correlations between the Chinese exchange market and stock market

Based on the daily price data of the Chinese Yuan (RMB)/US dollar exchange rate and the Shanghai Stock Composite Index, we conducted an empirical analysis of the cross-correlations between the Chinese exchange market and stock market using the multifractal cross-correlation analysis method. The results demonstrate the overall significance of the cross-correlation based on the analysis of a statistic. Multifractality exists in cross-correlations, and the cross-correlated behavior of small fluctuations is more persistent than that of large fluctuations. Moreover, using the rolling windows method, we find that the cross-correlations between the Chinese exchange market and stock market vary with time and are especially sensitive to the reform of the RMB exchange rate regime. The previous reduction in the flexibility of the RMB exchange rate in July 2008 strengthened the persistence of cross-correlations and decreased the degree of multifractality, whereas the enhancement of the flexibility of the RMB exchange rate in June 2010 weakened the persistence of cross-correlations and increased the multifractality. Finally, several relevant discussions are provided to verify the robustness of our empirical analysis.     

Test of the Fluctuation Relation in Lagrangian Turbulence on a Free Surface

The statistics of velocity divergence are studied for an assembly of particles that float on a closed turbulent fluid. Under an appropriate definition of entropy, the two-dimensional Lagrangian velocity divergence of a particle trajectory represents the local entropy rate , a random variable in time. The statistics of this rate, measured in the Lagrangian frame, are collected over a wide range of values. This permits a severe test of the fluctuation relation (FR) over a range that exceeds prior experiments, out to a regime beyond which the FR no longer holds. Notably, the probability density functions (PDF) of the dimensionless divergence σ _τ are strongly non-Gaussian. This work was supported by the National Science Foundation under grant number DMR-0201805.     

Fluctuations in apparent mass at the bottom of granular columns due to different arrangements

We report the fluctuations in apparent mass at the bottom of granular columns due to various configurations. It is found that the fluctuations decrease with the increase in the ratio of diameters of silo to grain. For the arrangement of different grain layers in a column, the higher fluctuations appear when the larger grains are stacked at the bottom layer while reversing the order of grain-layers leads to smaller fluctuations. We attribute this behavior to the randomness in the direction of frictional forces between the grains and the confining wall. Moreover, due to polydisperse media, the development of inhomogeneous force transmission in grains may cause this to happen.     

Characterizing abrupt changes in the stock prices using a wavelet decomposition method

Abrupt changes in the stock prices, either upwards or downwards, are usually preceded by an oscillatory behavior with frequencies that tend to increase as the moment of transition becomes closer. The wavelet decomposition methods may be useful for analysis of this oscillations with varying frequencies, because they provide simultaneous information on the frequency (scale) and localization in time (translation). However, in order to use the wavelet decomposition, certain requirements have to be satisfied, so that the linear and cyclic trends are eliminated by standard least squares techniques. The coefficients obtained by the wavelet decomposition can be represented in a graphical form. A threshold can then be established to characterize the likelihood of a short-time abrupt change in the stock prices. Actual data from the São Paulo Stock Exchange (Bolsa de Valores de São Paulo) were used in this work to illustrate the proposed method.     

Investigating the temporal variation of the scaling behavior in rainfall data measured in central Argentina by means of detrended fluctuation analysis

Investigation of the time variant scaling behavior of six monthly rainfall series recorded in central Argentina from 1860 to 2006 by using detrending fluctuation analysis (DFA) was performed. Changes in precipitation extremes are analyzed for several regions of Argentina using long-term monthly rainfall data (back to 1860) recorded by rain gauges extended for more than 10 latitude-degrees, from subtropical regions until 39^° S. A moving window was employed in order to analyze statistical changes. Three different types of time patterns can be distinguished: (i) eastern stations show visible crossovers between persistent and random behavior; (ii) north-western stations are characterized by random behavior approximately at any time and do not present visible crossovers between different types of scaling behaviors; (iii) one station (i.e. Corrientes) shows a peculiar pattern, since it is characterized by several crossovers from persistent to random behavior, indicating a more fluctuating time dynamics without a well defined trend. The obtained results can be interpreted in the context of the climatological conditions of Central Argentina, which is characterized by the continental heat low in the northwest region, by the subtropical rainforest in the eastern provinces and by a transition zone (from maritime to continental regime) fluctuating with the South Atlantic high-pressure cell.     

Volatilities, traded volumes, and the hypothesis of price increments in derivative securities

A detrended fluctuation analysis (DFA) is applied to the statistics of Korean treasury bond (KTB) futures from which the logarithmic increments, volatilities, and traded volumes are estimated over a specific time lag. In this study, the logarithmic increment of futures prices has no long-memory property, while the volatility and the traded volume exhibit the existence of the long-memory property. To analyze and calculate whether the volatility clustering is due to a inherent higher-order correlation not detected by with the direct application of the DFA to logarithmic increments of KTB futures, it is of importance to shuffle the original tick data of future prices and to generate a geometric Brownian random walk with the same mean and standard deviation. It was found from a comparison of the three tick data that the higher-order correlation inherent in logarithmic increments leads to volatility clustering. Particularly, the result of the DFA on volatilities and traded volumes can be supported by the hypothesis of price changes.     

Long-range dependence in tree-ring width time series of Austrocedrus Chilensis revealed by means of the detrended fluctuation analysis

By using the detrended fluctuation analysis and detrended moving average method, 823 time series of tree-ring widths in Austrocedrus Chilensis in Patagonia were analyzed. The tree-ring widths of A. Chilensis have been widely used for climatological studies. The results point out to the presence of significant scaling in the temporal fluctuations of tree-ring, which is not due to singular probability density function of the widths but due to the presence of long-range correlations. Such results are in good agreement with those concerning the evidence of long-range dependencies in weather time series.     

Fractal dimensionality and microscopic analysis of the dynamics in simple liquids

Summary The idea to evaluate the ?average fractal dimension? of the motion in a condensed phase system, on the basis of the analysis of the fractal properties of the trajectories of its microscopic components has been further developed. The fractal dimension of particle trajectories, evaluated through the correlation density integral, is formally related with the self-part of the dynamic structure factorG _s(r, t) (the self-part of the Van Hove function); so far a bridge between fractal and thermodynamical properties has been built up.

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Riassunto L’idea di stimare la ?dimensione frattale media? del moto in un sistema nella fase condensata è ulteriormente sviluppata mediante l’analisi delle proprietà frattali delle traiettorie delle componenti microscopiche. La dimensione frattale delle traiettorie delle particelle, stimata attraverso le correlazioni di densità, obbedisce ad una relazione formale con la self-part del fattore di struttura dinamicoG _s(r, t); in questo modo si mostra un legame tra le proprietà frattali e quelle termodinamiche.

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Резюме Развивается идея оценить ?среднюю фрактальную размерность? движения в конденсированной фазовой системе на основе анализа фрактальных свойств частицы траекторий для микроскопических компонент. Фрактальная размерность траекторий, определенная через корреляционный интеграл плотности, подчиняется формальному соотношеию с собтвенной частью динамического структурного фактораG _s(r,t) (собственная часть функции Ван Хава). Указывается связь между фрактальнымк и термодинамическими свойствами.

     

Cycles,scaling and crossover phenomenon in length of the day (LOD) time series

The dynamics of the temporal fluctuations of the length of the day (LOD) time series from January 1, 1962 to November 2, 2006 were investigated. The power spectrum of the whole time series has revealed annual, semi-annual, decadal and daily oscillatory behaviors, correlated with oceanic–atmospheric processes and interactions. The scaling behavior was analyzed by using the detrended fluctuation analysis (DFA), which has revealed two different scaling regimes, separated by a crossover timescale at approximately 23 days. Flicker-noise process can describe the dynamics of the LOD time regime involving intermediate and long timescales, while Brownian dynamics characterizes the LOD time series for small timescales.