scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

MODELING CROSS-CORRELATIONS OF TRAFFIC FLOW

2010 ◽  
Vol 20 (10) ◽  
pp. 3323-3328 ◽  
Author(s):  
PENGJIAN SHANG ◽  
KEQIANG DONG ◽  
SANTI KAMAE
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Power Law ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Large Increment ◽  
Active Research

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

scholarly journals Investigations of Broad Line Region Structure and Kinematics Using Variability

1989 ◽  
Vol 134 ◽  
pp. 93-95
Author(s):  
C. Martin Gaskell ◽  
Anuradha P. Koratkar ◽  
Linda S. Sparke
Keyword(s):  
Time Series ◽  
Cross Correlation ◽  
Sampling Interval ◽  
Broad Line ◽  
Line Flux ◽  
Line Region ◽  
Cross Correlations ◽  
The Mean ◽  
The Cross ◽  
The Continuum

Gaskell and Sparke (1986) showed that one can determine the sizes of BLRs more accurately that the mean sampling interval by cross-correlating the continuum flux time series with a line flux time series. The position of the peak in the cross-correlation function (CCF) and its shape give an indication of the BLR size. The technique is explained in detail in Gaskell and Peterson (1987). The widely propagated misunderstanding is that the method involves simply interpolating both time series and cross-correlating them (in which case the CCF is dominated by the cross-correlations of “made-up” data). Actually the method involves cross correlating the observed points in one time series (continuum, say) with the linear interpolations of the other series (line flux). The line flux time series must always be smoother than the continuum time series it is derived from. We have usually employed the method with the interpolation done both ways round and averaged them (to reduce errors due to the interpolation) and we can intercompare the two results (to investigate errors).

Multiscale Multifractal Detrended Cross-Correlation Analysis of High-Frequency Financial Time Series

2019 ◽  
Vol 18 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Jingjing Huang ◽  
Danlei Gu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
High Frequency ◽  
Cross Correlation ◽  
Financial Time Series ◽  
Chinese Market ◽  
Change Of Scale ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross

In order to obtain richer information on the cross-correlation properties between two time series, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). This method is based on the Hurst surface and can be used to study the non-linear relationship between two time series. By sweeping through all the scale ranges of the multifractal structure of the complex system, it can present more information than the multifractal detrended cross-correlation analysis (MF-DCCA). In this paper, we use the MM-DCCA method to study the cross-correlations between two sets of artificial data and two sets of 5[Formula: see text]min high-frequency stock data from home and abroad. They are SZSE and SSEC in the Chinese market, and DJI and NASDAQ in the US market. We use Hurst surface and Hurst exponential distribution histogram to analyze the research objects and find that SSEC, SZSE and DJI, NASDAQ all show multifractal properties and long-range cross-correlations. We find that the fluctuation of the Hurst surface is related to the positive and negative of [Formula: see text], the change of scale range, the difference of national system, and the length of time series. The results show that the MM-DCCA method can give more abundant information and more detailed dynamic processes.

Generation of synthetic cross-correlated water demand time series

2013 ◽  
Vol 13 (4) ◽  
pp. 977-986 ◽  
Author(s):  
N. Ansaloni ◽  
S. Alvisi ◽  
M. Franchini
Keyword(s):  
Time Series ◽  
Water Demand ◽  
Distribution System ◽  
Water Distribution ◽  
Cross Correlation ◽  
Time Lags ◽  
Cross Correlations ◽  
The Cross ◽  
Water Districts

This paper presents a procedure for generating synthetic district-level series of hourly water demand coefficients cross-correlated in space (between districts) and time. The procedure consists of two steps: (1) generation of hourly water demand coefficients which respect, for each hour of the day, pre-assigned means and variances; and (2) introduction of the cross-correlation at different time lags through the application of a method which implies the reordering of the data generated at step 1. The procedure was applied to a case study of the Ferrara water distribution system with the aim of generating cross-correlated synthetic series of hourly water demand coefficients for the 19 water districts making it up. It was observed that the application of the method for introducing the cross-correlation (step 2) causes numerical problems when a large number of water districts are involved and the cross-correlations are considered at many time lags; this problem is solved by carrying out an appropriate regularization of the observed cross-correlation matrix. The results obtained show that overall the proposed procedure constitutes a valid tool for generating synthetic water demand time series with pre-assigned characteristics in terms of means, variances and cross-correlation at different time lags.

CROSS-CORRELATION ANALYSIS IN MIXED TRAFFIC FLOW TIME SERIES

2011 ◽  
Vol 25 (13) ◽  
pp. 1823-1832 ◽  
Author(s):  
S. Y. XU ◽  
H. J. SUN ◽  
J. J. WU
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Correlation Coefficient ◽  
Linear Correlation ◽  
Cross Correlation ◽  
Flow Time ◽  
Mixed Traffic ◽  
Mixed Traffic Flow ◽  
Vehicle Density ◽  
The Cross

In this paper, we investigate the complexity behind the mixed traffic flow time series generated by multi-lane cellular automaton model. Throughout the paper, the cross-correlation coefficient is introduced to characterize the time series. It is found that there exists a critical vehicle density S, when S < S1 and the ratio of slow vehicle R > 0.01, the cross-correlation coefficient r is larger than 0.5, which indicates a significant linear correlation. Otherwise, the cross-correlation coefficient r < 0.5 which corresponds to a weak linear correlation. That is to say, the vehicle density plays an important role in the cross-correlation coefficient. Additionally, we also found that the asymmetric lane-change probability has no great influence on the cross-correlation coefficient.

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

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Keqiang Dong ◽  
Xiaojie Gao
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Correlation Coefficient ◽  
Nonlinear Interaction ◽  
Cross Correlation ◽  
Nonstationary Time Series ◽  
New Method ◽  
Nonlinear Interactions ◽  
Cross Correlation Analysis ◽  
The Cross

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.

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

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andrea de Almeida Brito ◽  
Heráclio Alves de Araújo ◽  
Gilney Figueira Zebende
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Solar Energy ◽  
Correlation Coefficient ◽  
Air Temperature ◽  
Cross Correlation ◽  
Global Solar Radiation ◽  
Meteorological Variables ◽  
Hourly Data ◽  
Cross Correlations

AbstractDue 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, $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2. 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 $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2 to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}$$DMCx2=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.

Does the weather affect the Chinese stock markets? Evidence from the analysis of DCCA cross-correlation coefficient

2014 ◽  
Vol 29 (01) ◽  
pp. 1450236 ◽  
Author(s):  
Guangxi Cao ◽  
Yan Han
Keyword(s):  
Correlation Coefficient ◽  
Stock Markets ◽  
Cross Correlation ◽  
Sunshine Duration ◽  
Statistical Test ◽  
Nonlinear Method ◽  
Weather Variables ◽  
Chinese Stock Markets ◽  
The Cross ◽  
The Relationship

Recent studies confirm that weather affects the Chinese stock markets, based on a linear model. This paper revisits this topic using DCCA cross-correlation coefficient (ρ DCCA (n)), which is a nonlinear method, to determine if weather variables (i.e., temperature, humidity, wind and sunshine duration) affect the returns/volatilities of the Shanghai and Shenzhen stock markets. We propose an asymmetric ρ DCCA (n) by improving the traditional ρ DCCA (n) to determine if different cross-correlated properties exist when one time series trending is either positive or negative. Further, we improve a statistical test for the asymmetric ρ DCCA (n). We find that cross-correlation exists between weather variables and the stock markets on certain time scales and that the cross-correlation is asymmetric. We also analyze the cross-correlation at different intervals; that is, the relationship between weather variables and the stock markets at different intervals is not always the same as the relationship on the whole.

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