Detrended Cross-correlation Research Articles

Multiscale detrended cross-correlation coefficient: estimating coupling in non-stationary neurophysiological signals

The brain consists of a vastly interconnected network of regions, the connectome. By estimating the statistical interdependence of neurophysiological time series, we can measure the functional connectivity (FC) of this connectome. Pearson’s correlation (rP) is a common metric of coupling in FC studies. Yet rP does not account properly for the non-stationarity of the signals recorded in neuroimaging. In this study, we introduced a novel estimator of coupled dynamics termed multiscale detrended cross-correlation coefficient (MDC3). Firstly, we showed that MDC3 had higher accuracy compared to rP and lagged covariance using simulated time series with known coupling, as well as simulated functional magnetic resonance imaging (fMRI) signals with known underlying structural connectivity. Next, we computed functional brain networks based on empirical magnetoencephalography (MEG) and fMRI. We found that by using MDC3 we could construct networks of healthy populations with significantly different properties compared to rP networks. Based on our results, we believe that MDC3 is a valid alternative to rP that should be incorporated in future FC studies.

Cryptocurrencies Are Becoming Part of the World Global Financial Market

In this study the cross-correlations between the cryptocurrency market represented by the two most liquid and highest-capitalized cryptocurrencies: bitcoin and ethereum, on the one side, and the instruments representing the traditional financial markets: stock indices, Forex, commodities, on the other side, are measured in the period: January 2020-October 2022. Our purpose is to address the question whether the cryptocurrency market still preserves its autonomy with respect to the traditional financial markets or it has already aligned with them in expense of its independence. We are motivated by the fact that some previous related studies gave mixed results. By calculating the q-dependent detrended cross-correlation coefficient based on the high frequency 10 s data in the rolling window, the dependence on various time scales, different fluctuation magnitudes, and different market periods are examined. There is a strong indication that the dynamics of the bitcoin and ethereum price changes since the March 2020 COVID-19 panic is no longer independent. Instead, it is related to the dynamics of the traditional financial markets, which is especially evident now in 2022, when the bitcoin and ethereum coupling to the US tech stocks is observed during the market bear phase. It is also worth emphasizing that the cryptocurrencies have begun to react to the economic data such as the Consumer Price Index readings in a similar way as traditional instruments. Such a spontaneous coupling of the so far independent degrees of freedom can be interpreted as a kind of phase transition that resembles the collective phenomena typical for the complex systems. Our results indicate that the cryptocurrencies cannot be considered as a safe haven for the financial investments.

Video-based marker-free tracking and multi-scale analysis of mouse locomotor activity and behavioral aspects in an open field arena: A perspective approach to the quantification of complex gait disturbances associated with Alzheimer's disease.

Complex gait disturbances represent one of the prominent manifestations of various neurophysiological conditions, including widespread neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Therefore, instrumental measurement techniques and automatic computerized analysis appears essential for the differential diagnostics, as well as for the assessment of treatment effectiveness from experimental animal models to clinical settings. Here we present a marker-free instrumental approach to the analysis of gait disturbances in animal models. Our approach is based on the analysis of video recordings obtained with a camera placed underneath an open field arena with transparent floor using the DeeperCut algorithm capable of online tracking of individual animal body parts, such as the snout, the paws and the tail. The extracted trajectories of animal body parts are next analyzed using an original computerized methodology that relies upon a generalized scalable model based on fractional Brownian motion with parameters identified by detrended partial cross-correlation analysis. We have shown that in a mouse model representative movement patterns are characterized by two asymptotic regimes characterized by integrated 1/f noise at small scales and nearly random displacements at large scales separated by a single crossover. More detailed analysis of gait disturbances revealed that the detrended cross-correlations between the movements of the snout, paws and tail relative to the animal body midpoint exhibit statistically significant discrepancies in the Alzheimer's disease mouse model compared to the control group at scales around the location of the crossover. We expect that the proposed approach, due to its universality, robustness and clear physical interpretation, is a promising direction for the design of applied analysis tools for the diagnostics of various gait disturbances and behavioral aspects in animal models. We further believe that the suggested mathematical models could be relevant as a complementary tool in clinical diagnostics of various neurophysiological conditions associated with movement disorders.

Correlation and causality between carbon and energy markets: a complexity perspective.

Global warming obliges humans to focus on the relationships between carbon and energy markets. This study considers the relationship between carbon and energy markets from a complexity perspective. Chinese carbon prices and four energy indexes are selected as empirical variables. First, the complexities of carbon and energy markets are measured by multi-scale fuzzy entropy. The critical time delay of the series is then obtained by maximizing the Pearson coefficients between these markets. Further, analysis of the detrended cross-correlation coefficient confirms the existence of time delay. Finally, transfer entropy is applied to investigate the causality pertaining to dynamic complexity. Results of fuzzy entropy analysis reveal that the carbon market has lower complexity than energy markets. Meanwhile, multi-scale results indicate greater complexity on the small time scales in all markets than on the large time scales. The critical time delay is found to be about 50, which maximizes the correlation coefficient. Finally, causality between carbon and energy markets varies. Expectations in the carbon market impact oil gas and coal markets; electricity and new energy affect the carbon market; and cross-causality exists in the relationship between coal and carbon markets. The participants should focus on the information transmission between carbon and energy markets.

Long-Term Correlations and Cross-Correlations in Meteorological Variables and Air Pollution in a Coastal Urban Region

In this work, we evaluated the evolution of some atmospheric pollutants (O3, NOx and PM10) over time and their relationship with four different climate variables (solar irradiation, air temperature, relative humidity and wind speed). To this end, we assessed the long-range dependence of those concentrations with a Detrended Fluctuation Analysis (DFA) and analyzed the cross-correlation of such dependence with the climate variables through a Detrended Cross-Correlation Coefficient Analysis (ρDCCA). The results show that air pollution tends to increase over time, impairing air quality and likely affecting human health. The results indicate a cross-correlation between air pollution and the climatic variables, which persisted for a certain period, with a greater correlation between O3 concentration and wind, mainly temperature, and a negative correlation with humidity for all monitoring stations. Moreover, unlike O3 and PM10, NOx concentrations always had a persistent behavior in the region of study for the entire analyzed period.

Statistical Approach to Study the Relationship Between Stock Market Indexes by Multiple DCCA Cross-Correlation Coefficient

In this paper, we propose to analyze multiple cross-correlation between six stock market indexes (Dow Jones Industrial Average, Nasdaq Composite, DAX Performance, FTSE 100, S&P/TSX Composite and Nikkei 225) based on the multiple detrended cross-correlation coefficient, [Formula: see text]. Due to its importance and long existence, we will have as the base index, acting as dependent variable, the Dow Jones Industrial Average, which will be compared with the other five indexes in all possible combinations. In addition to calculating the [Formula: see text] for all combinations with Dow Jones, we will also infer the relative strength of each index in relation to the whole, and this will be done here through an unprecedented map of relative strength. With this map it will be possible to verify that the Nikkei 225 index has less weight for all time-scales and also all combinations, and that there is better distribution in the Nasdaq and DAX combination. Finally, we present more possibilities for this application throughout the paper.

Spillover effects and nonlinear correlations between carbon emissions and stock markets: An empirical analysis of China's carbon-intensive industries

This study analyzes the correlations between carbon emissions and related industry stock markets in China. We propose a carbon-intensive industry index firstly. According to the Spillover Index, the two markets interact and the carbon-intensive stock market acts as an information receiver in most cases. We apply the Multifractal Cross-Correlation Analysis, Detrended Cross-Correlation Coefficient, and the modified Time-lagged Detrended Cross-Correlation to characterize the nonlinear correlations between carbon allowance price returns and the stock returns of carbon-intensive industries. The carbon emission trading market is found to be more volatile and inefficient than the stock market; the properties of the carbon trading pilot explain the direction and magnitude of the nonlinear correlations. The level of intervention by the government authority affects the magnitude of correlations; the strongest dynamic return spillovers and the most persistent time-lag cross-correlations were observed in the Shenzhen pilot—the most market-oriented carbon emission trading pilot in China. The allowance allocation method plays an important role in deciding the direction of the nonlinear correlations. Our empirical results show the stock returns of carbon-intensive industries and the carbon allowance price returns were positively cross-correlated in Shenzhen and Shanghai pilots, while the cross-correlations were negative in Beijing, Guangdong, and Hubei pilots.

Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes.

Assessing power-law cross-correlations between a pair – or among a set – of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications – such as mental state monitoring or financial forecasting – call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.

Detrended Correlogram Method for Non-Stationary Time-Series Analysis

A correlogram is a statistical tool that is used to check time-series memory by computing the auto-correlation coefficient as a function of the time lag. If the time-series has no memory, then the auto-correlation must be close to zero for any time lag, otherwise if there is a memory, then the auto-correlations must be significantly different from zero. Therefore, based on the robust detrended cross-correlation coefficient, [Formula: see text], we propose the detrended correlogram method in this paper, which will be tested for some time-series (simulated and empirical). This new statistical tool is able to visualize a complete map of the auto-correlation for many time lags and time-scales, and can therefore analyze the memory effect for any time-series.

Correlações em séries temporais de preços de frango, soja e milho

A evolução do mercado agrícola brasileiro alterou o processo de produção, exportação e consumo de commodities alimentares. Com isso, novos estudos acerca da relação entre o mercado de alimentos e outros mercados foram desenvolvidos, buscando explicar a ligação entre os preços de commodities agrícolas e não agrícolas. Visando contribuir para esse estudo, foram investigadas as correlações de longo prazo entre os preços de commodities agrícolas brasileiras, utilizando técnicas de Econofísica. Analisaram-se então as séries diárias de preços e retorno de preços da carne de frango, soja e milho, registrados entre 02/08/2004 e 16/06/2017 pelo Centro de Estudos Avançados em Economia Aplicada / Escola Superior de Agricultura Luiz de Queiroz / Universidade de São Paulo - CEPEA/ESALQ/USP. As correlações entre as séries temporais foram investigadas utilizando os métodos Detrended Fluctuation Analysis (DFA) e Detrended Cross Correlation Analysis (DCCA), para calcular o Detrended Cross Correlation Coefficient (DCCA Coefficient), que serve para quantificar correlações de longo prazo entre séries temporais não estacionárias. Os resultados obtidos apontam para a ausência de correlações nas escalas de até 30 dias e, para escalas maiores, acusam correlações mais fortes entre os preços de frango e milho que entre os preços de frango e soja. Após a crise alimentar de 2008, entretanto, as correlações entre as séries diárias de retorno de preços do frango e do milho diminuíram, enquanto que, entre as de frango e soja, aumentaram nas escalas menores e diminuíram nas escalas maiores.

Detrended multiple cross-correlation coefficient with sliding windows approach

In this paper we implemented the detrended multiple cross-correlation coefficient with sliding windows approach in order to measure multiple cross-correlation between time series as a function of time scale n, and a sliding time τ. Faced with several non-stationary time series, a fixed size window will be defined by w, and the coefficients DMCx2 are calculated for different time scales (4≤n≤w4) and time τ. Following this methodology, it was possible to set up a DMCx2 cross-correlation color map for a simulated (random) and an empirical case. This new color map with sliding windows shows the time scale and the current day for a cross-correlation analysis. In this way, it is possible to analyze the multiple cross-correlation between three or more variables in different areas of knowledge, such as economics and finance.

Statistical properties of the detrended multiple cross-correlation coefficient

Cross-correlations are ubiquitous in nonstationary multivariable systems. By using detrended cross-correlation (DCCA) technique, recently a new multiple cross-correlation coefficient DMC was proposed to quantity the correlation between multivariate and a target variable. We studied the statistical properties of DMC in detail. More specifically, we first proved that 0≤DMC≤1, and then deduced that the DMC is approximately χ2 distributed for overlapping windows with different window size. In addition, the range of DMC was determined numerically by statistical test, where the multiple correlations can be regarded as statistically significant. Furthermore, we discussed the influence of the cross-correlation among the target variable and independent variables on DMC. Finally, by utilizing this statistical test on financial system and environment data, we found that the US dollar index affects international gold spot prices and West Texas Intermediate oil price greatly, and PM2.5 dominates in Beijing’s AQI system.

Characterization of variability and trends in daily precipitation and temperature extremes in the Horn of Africa

Modeling of extreme weather conditions is an important issue in environmental risk assessment, management and protection. In this paper, Annual and monthly maxima of daily temperature and rainfall data dating from 1901–2016 and 1950–2018 are characterized for nine countries within the greater horn of Africa. The generalized extreme value (GEV) distribution is fitted to the data sets from each of the nine countries using the method of maximum likelihood. Both the location and scale parameters of the GEV is formulated as a function of time to account for variability and trends in the extremes of temperature and rainfall so that their future behavior can be predicted. Based on our results, We provide return levels for the years 2, 10, 50 100, and 200 which could be used as measures of flood protection. To understand the spatial cross-correlation patterns on different time scales in each country and how rainfall and temperature are related to agricultural variables, we utilize the detrended cross-correlation coefficient(ρDCCA) and its generalization, (DMCx2) to account for that, respectively. Given the results of the (DMCx2) and the fact that climate extremes pose a huge threat to agriculture and food security, we employed copula based models to describe the structure of dependence between climatic variables and the crop related variables such as yield and production quantity. The results from the copula analysis show that irrespective of the country, climatic factors and the agricultural products(production/yield) the strongest dependence is demonstrated by the pairs involving cereal crops, while the weakest dependence is characterized by the pairs involving regular potato.

Statistical test for Multiple Detrended Cross-Correlation Coefficient

In this paper, we proposed a statistical test for the Multiple Detrended Correlation Coefficient DMCx2. The DMCx2 is a measure of total association between the dependent variable, Y, with other p independent variables, X all with the same length N. DMCx2 is based on the generalization of the ρ(Xi,Xj) cross-correlation coefficient. With this methodology, it is possible to evaluate the statistical significance of DMCx2 for different levels confidence. Findings on this research show that rejection or non-rejection of the null hypothesis of DMCx2 also depends on the size N of the series and the time scale n evaluated. Our findings also show a behavior pattern in the critical values of DMCx2. Fixing the size of the series (N), as the size of the time scale n increases, the critical values tend to increase.

Higher-Order Multifractal Detrended Partial Cross-Correlation Analysis for the Correlation Estimator

In this paper, we develop a new method to measure the nonlinear interactions between nonstationary time series based on the detrended cross-correlation coefficient analysis. We describe how a nonlinear interaction may be obtained by eliminating the influence of other variables on two simultaneous time series. By applying two artificially generated signals, we show that the new method is working reliably for determining the cross-correlation behavior of two signals. We also illustrate the application of this method in finance and aeroengine systems. These analyses suggest that the proposed measure, derived from the detrended cross-correlation coefficient analysis, may be used to remove the influence of other variables on the cross-correlation between two simultaneous time series.

Detrended Multiple Cross-Correlation Coefficient applied to solar radiation, air temperature and relative humidity

Due to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the cross-correlations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global cross-correlation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended Cross-Correlation Coefficient, ρDCCA, and subsequently with the recently developed Multiple Detrended Cross-Correlation Coefficient, {boldsymbol{DM}}{{boldsymbol{C}}}_{{bf{x}}}^{{bf{2}}}. We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρDCCA was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied {boldsymbol{DM}}{{boldsymbol{C}}}_{{bf{x}}}^{{bf{2}}} to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that {boldsymbol{DM}}{{boldsymbol{C}}}_{{bf{x}}}^{{bf{2}}}={bf{1}} (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.

DCCA cross-correlation analysis in time-series with removed parts

In this paper we analyze the effect of removing pieces in time-series with long range-memory by DFA method and detrended cross-correlation coefficient. To achieve this purpose, initially simulated time-series are produced by ARFIMA process (long time dependence). From these simulated time-series cuts and removals are produced. The results show that for up to 50% of removed parts, compared to the original time-series, there is no change in the final results for detrended auto and cross-correlations. Therefore, with this paper we show that the DFA method and the detrended cross-correlation coefficient are robust for time-series analysis even for time-series with removed parts. This result ensures that these methods can be applied to real time-series, which in many cases lacks measurement for a variety of reasons and causes.

Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights

In this paper, the utility and the correlation technique of the detrended cross-correlation analysis and the combined detrended cross-correlation analysis methods are treated for the stochastic properties of the random walk and the Lévy flight via nucleotide sequence data. Data are extracted definitely from twelve genomic DNA sequences (HUMHBB 1-6, Amazonmolly, Bushbaby, Cow, Dolphin, Elephant, and Tarsier) of the GenBank databank. We mainly simulate and analyze scaling exponents for three methods in 1D and 2D random walks and Lévy flights. To compare each other between one gene and the other gene in the twelve genomic DNA sequences, the value of the detrended cross-correlation coefficient ρDCCA in {HUMHBB3} and {Dolphin} genes is shown the largest value 0.214 in the 1D Lévy flight with μ=1.5 compared to other sets. The detrended cross-correlation coefficient ρDCCA in {HUMHBB4} and {HUMHBB6} genes is shown the smallest value -0.231 in the 1D Lévy flight with μ=1.5. We particularly find that the combined detrended cross-correlation coefficient ρCDCCA in the two cases of {HUMHBB3}+{Bushbaby} and {HUMHBB6}+{Dolphin} has the largest value 0.331 in the 1D random walk compared to other sets, while that in {HUMHBB3}+{Tarsier} and {HUMHBB4}+{Elephant} has the smallest value -0.295 in the 1D Lévy flight with μ=1.5.

Application of an Improved Correlation Method in Electrostatic Gait Recognition of Hemiparetic Patients.

Hemiparesis is one of the common sequelae of neurological diseases such as strokes, which can significantly change the gait behavior of patients and restrict their activities in daily life. The results of gait characteristic analysis can provide a reference for disease diagnosis and rehabilitation; however, gait correlation as a gait characteristic is less utilized currently. In this study, a new non-contact electrostatic field sensing method was used to obtain the electrostatic gait signals of hemiplegic patients and healthy control subjects, and an improved Detrended Cross-Correlation Analysis cross-correlation coefficient method was proposed to analyze the obtained electrostatic gait signals. The results show that the improved method can better obtain the dynamic changes of the scaling index under the multi-scale structure, which makes up for the shortcomings of the traditional Detrended Cross-Correlation Analysis cross-correlation coefficient method when calculating the electrostatic gait signal of the same kind of subjects, such as random and incomplete similarity in the trend of the scaling index spectrum change. At the same time, it can effectively quantify the correlation of electrostatic gait signals in subjects. The proposed method has the potential to be a powerful tool for extracting the gait correlation features and identifying the electrostatic gait of hemiplegic patients.

Multifractal cross-correlations between the world oil and other financial markets in 2012–2017

Statistical and multiscaling characteristics of WTI Crude Oil futures prices expressed in US dollar in relation to the most traded currencies as well as to gold futures and to the E-mini S&P500 futures prices on 5 min intra-day recordings in the period January 2012–December 2017 are studied. It is shown that in most of the cases the tails of return distributions of the considered financial instruments follow the inverse cubic power law. The only exception is the Russian ruble for which the distribution tail is heavier and scales with the exponent close to 2. From the perspective of multiscaling the analysed time series reveal the multifractal organization with the left-sided asymmetry of the corresponding singularity spectra. Even more, all the considered financial instruments appear to be multifractally cross-correlated with oil, especially on the level of medium-size fluctuations, as the multifractal cross-correlation analysis carried out by means of the multifractal cross-correlation analysis (MFCCA) and detrended cross-correlation coefficient ρq show. The degree of such cross-correlations is however varying among the financial instruments. The strongest ties to the oil characterize currencies of the oil extracting countries. Strength of this multifractal coupling appears to depend also on the oil market trend. In the analysed time period the level of cross-correlations systematically increases during the bear phase on the oil market and it saturates after the trend reversal in 1st half of 2016. The same methodology is also applied to identify possible causal relations between considered observables. Searching for some related asymmetry in the information flow mediating cross-correlations indicates that it was the oil price that led the Russian ruble over the time period here considered rather than vice versa.