Detrended Cross-correlation Analysis Cross-correlation Research Articles

Dynamical Characteristics in Time Series Between PM10 and Wind Speed

We study the temporal variation characteristics of PM10 and wind velocity in eight South Korean cities. We employ the detrended cross-correlation analysis (DCCA) method to extract the overall tendency of the hourly variation. We ascertain from three-daily and one-weekly intervals that Busan has the negative largest, while Donghae has the positive largest in the DCCA cross-correlation coefficient between PM10 and wind velocity. As a result of Asian dust events, the cross-correlation is statistically significant for the hourly time series data less than two days. Particularly, we discuss whether a cross-correlation is statistically significant or not from random number surrogation and shuffled time series surrogation

Detrended cross correlation analysis (DCCA) of radon, thoron, temperature and pressure time series data

Non-linear processes evolving within earth crust and in atmosphere gives complex time series and extracting meaningful physical information from such data is not easy without development and practice of modern computational techniques. Detrended fluctuation analysis (DFA), and detrended cross correlation analysis (DCCA), are used to explore long-range correlations and characterization of correlated data of more than one non-stationary time series. We present results of DFA, and DCCA techniques applied on radon, thoron, temperature and pressure time series. Time series data of each series have been decomposed for each season and seasonal periodicities have been removed. DFA and DCCA techniques have been employed on the deseasonalized data. For all four seasons, DFA scaling exponent () and correlation exponent () have been calculated for radon, thoron, temperature and pressure time series. The results of ‘’ and ‘r’, for each of the time series have been used for finding the existence of persistency in processes and investigation of long-range correlations. Largely, these results indicate that the cross-correlation relationship between observed times series for each season is not of simply power-law type. Detrended Cross Correlation Analysis between different time series shows persistent behavior. In order to quantify the level of cross-correlations, we computed the DCCA cross-correlation coefficient

Multi-scale cross-correlation analysis of temporal and spatial seismic data

We investigate the cross-correlation relationships between temporal and spatial seismic data by employing detrended cross-correlation analysis (DCCA) and temporal evolution of detrended cross-correlation analysis (TDCCA). The mentioned data are the series of inter-earthquakes times (IET) and inter-earthquakes distances (IED) between consecutive earthquakes in California and Sumatra regions from 1990 to 2013. Through cross-correlation test, we find long-range cross-correlation between IET and IED. We find the DCCA cross-correlation coefficient ρDCCA between them is significantly positive with the change of scale. The TDCCA between two series demonstrates cross-correlations on different window size scales over time. Strong cross-correlation levels between IET and IED on different window sizes are observed for the time periods after the big earthquakes occurred, while there are weak or no cross-correlation before and after the periods.

Neural network and regression methods for optimizations between two meteorological factors

This paper is concerned with the temporal variation characteristics of two meteorological factors (temperature and humidity) in four metropolitan cities (Seoul, Busan, Daegu, Daejeon) in South Korea. Data are extracted from seven years (2008 to 2014) of hourly time series data in meteorological offices of the Korea Meteorological Administration. Using the detrended cross-correlation analysis (DCCA) method, the DCCA coefficient of temperature is compared to that of humidity from daily time series data during four seasons in the four metropolitan cities. In particular, as window size s increases, the DCCA cross-correlation coefficient approaches 0.034 at a time lag of 14 days in the case of spring in Seoul. We find the weak cross-correlation between temperature and humidity at different time lags of 14, 21 and 28 days in spring in Seoul, and the errors ET in the ANN are relatively larger values than that of any other season in both the ANN and the MRM. Particularly, in the ANN model, there exist relatively a large error value of temperature as the characteristics of the non-stationary, deterministically chaotic and noisy meteorological data extracted for the short-term prediction rather than the long-term prediction.

Instability of horizontal oil-water flows based on the signal-dependent complex admittance representations

Horizontal oil-water two-phase flows are characterized by unstable motions of interfacial wave and entrained droplets. An experiment of horizontal oil-water flow was made in an acrylic pipe with an inner diameter of 20 mm. A measurement system of concave capacitance sensor is designed to detect the real and imaginary parts of flow complex admittance. An Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) of the complex admittance angle is used to characterize the flow instability in terms of total energy. A detrended cross-correlation analysis (DCCA) of the oil-water complex admittance is conducted to investigate the instability multi-scale flow structures. The cross-correlation coefficients at large and small scales enable to characterize the instability of the oil-water interface and the entrained droplets in continuous phases, respectively. The result suggests that the DCCA cross-correlation coefficients and the total energy extracted from AOK TFR are accordant in uncovering the instability of horizontal oil-water flows.

DCCA cross-correlation coefficients reveals the change of both synchronization and oscillation in EEG of Alzheimer disease patients

Alzheimer’s disease (AD) is a degenerative disorder of neural system that affects mainly the older population. Recently, many researches show that the EEG of AD patients can be characterized by EEG slowing, enhanced complexity of the EEG signals, and EEG synchrony. In order to examine the neural synchrony at multi scales, and to find a biomarker that help detecting AD in diagnosis, detrended cross-correlation analysis (DCCA) of EEG signals is applied in this paper. Several parameters, namely DCCA coefficients in the whole brain, DCCA coefficients at a specific scale, maximum DCCA coefficient over the span of all time scales and the corresponding scale of such coefficients, were extracted to examine the synchronization, respectively. The results show that DCCA coefficients have a trend of increase as scale increases, and decreases as electrode distance increases. Comparing DCCA coefficients in AD patients with healthy controls, a decrease of synchronization in the whole brain, and a bigger scale corresponding to maximum correlation is discovered in AD patients. The change of max-correlation scale may relate to the slowing of oscillatory activities. Linear combination of max DCCA coefficient and max-correlation scale reaches a classification accuracy of 90%. From the above results, it is reasonable to conclude that DCCA coefficient reveals the change of both oscillation and synchrony in AD, and thus is a powerful tool to differentiate AD patients from healthy elderly individuals.

Temporal-spatial cross-correlation analysis of non-stationary near-surface wind speed time series

Temporal-spatial cross-correlation analysis of non-stationary wind speed time series plays a crucial role in wind field reconstruction as well as in wind pattern recognition. Firstly, the near-surface wind speed time series recorded at different locations are studied using the detrended fluctuation analysis (DFA), and the corresponding scaling exponents are larger than 1. This indicates that all these wind speed time series have non-stationary characteristics. Secondly, concerning this special feature (i.e., non-stationarity) of wind signals, a cross-correlation analysis method, namely detrended cross-correlation analysis (DCCA) coefficient, is employed to evaluate the temporal-spatial cross-correlations between non-stationary time series of different anemometer pairs. Finally, experiments on ten wind speed data synchronously collected by the ten anemometers with equidistant arrangement illustrate that the method of DCCA cross-correlation coefficient can accurately analyze full-scale temporal-spatial cross-correlation between non-stationary time series and also can easily identify the seasonal component, while three traditional cross-correlation techniques (i.e., Pearson coefficient, cross-correlation function, and DCCA method) cannot give us these information directly.

Long memory of abnormal investor attention and the cross-correlations between abnormal investor attention and trading volume, volatility respectively

Abstract Taking Baidu Index as a proxy for abnormal investor attention (AIA), the long memory property in the AIA of Shanghai Stock Exchange (SSE) 50 Index component stocks was empirically investigated using detrended fluctuation analysis (DFA) method. The results show that abnormal investor attention is power-law correlated with Hurst exponents between 0.64 and 0.98. Furthermore, the cross-correlations between abnormal investor attention and trading volume, volatility respectively are studied using detrended cross-correlation analysis (DCCA) and the DCCA cross-correlation coefficient ( ρ D C C A ). The results suggest that there are positive correlations between AIA and trading volume, volatility respectively. In addition, the correlations for trading volume are in general higher than the ones for volatility. By carrying on rescaled range analysis (R/S) and rolling windows analysis, we find that the results mentioned above are effective and significant.

Effect of Weather on Agricultural Futures Markets on the Basis of DCCA Cross-Correlation Coefficient Analysis

This study investigates the correlation between weather and agricultural futures markets on the basis of detrended cross-correlation analysis (DCCA) cross-correlation coefficients and [Formula: see text]-dependent cross-correlation coefficients. In addition, detrended fluctuation analysis (DFA) is used to measure extreme weather and thus analyze further the effect of this condition on agricultural futures markets. Cross-correlation exists between weather and agricultural futures markets on certain time scales. There are some correlations between temperature and soybean return associated with medium amplitudes. Under extreme weather conditions, weather exerts different influences on different agricultural products; for instance, soybean return is greatly influenced by temperature, and weather variables exhibit no effect on corn return. Based on the detrending moving-average cross-correlation analysis (DMCA) coefficient and DFA regression results are similar to that of DCCA coefficient.

A detrended cross-correlation analysis of meteorological and API data in Nanjing, China

The cross correlation between daily meteorological data and air pollution index (API) records in Nanjing during the past 12 years is studied by means of a detrended cross-correlation analysis (DCCA). In this study, we use statistical significance tests and power-law statistical tests to verify cross correlation between meteorological data and the API. Through calculating the DCCA cross correlation coefficient ρDCCA, we intend to obtain a range of cross correlation levels between the meteorological data and the API at different time scales. Utilizing the multifractal detrended cross correlation analysis (MF-DCCA) and algorithm-multifractal cross correlation analysis (MF-CCA) proposed by Oświecimka, we observe multifractal cross-correlation behavior between meteorological factors and the API. Our results show a cross correlation between meteorological factors and the API in Nanjing. The cross-correlation between diurnal temperature ranges and the API is persistent at studied time scales, while the cross correlations of wind speed, relative humidity, and precipitation with the API are anti-persistent at studied time scales. Next, a cross correlation of temperature with the API finds persistent cross correlation at smaller time scales, and anti-persistent cross-correlation at larger time scales; the cross correlation of atmospheric pressure with the API, however, results in anti-persistent cross correlation at smaller time scales, and persistent cross correlation at larger time scales. The MF-DCCA demonstrates that all underlying fluctuations have a weak multifractal nature where one scaling exponent is obtained. However, the MF-CCA suggests that some crossovers exist in the cross-correlation fluctuation function in terms of time scales of temperature and atmospheric pressure versus the API. The MF-CCA method is more subtle and suitable for reflecting the cross correlation of the two given time series. Compared with a traditional correlation analysis, the DCCA can uncover more cross-correlation information between API and meteorological factors. Therefore, the DCCA is also recommended as a comparatively reliable method for detecting the correlations between the API and meteorological data, and can also be useful for our understanding of the cross correlation between air quality and meteorological elements.

Different spatial cross-correlation patterns of temperature records over China: A DCCA study on different time scales

Daily mean temperature records over China during the past 50 years are studied by means of detrended cross-correlation analysis (DCCA). Taking Beijing as a center, we calculate the DCCA cross-correlation coefficient σDCCA between the temperatures in Beijing and those in other stations. After a statistical significance test, spatial cross-correlation patterns on different time scales are shown in this paper. We find the spatial cross-correlation patterns can vary with time scales. On small time scale of one week to one month, only the temperatures in nearby regions have close relations with that in Beijing, while on larger time scale of intra or inter-seasonal, temperatures in most of the regions, especially in the northeast show high level cross-correlations with that in Beijing. The southwest plateau (including the Tibetan Plateau and the YunGui Plateau) is a special region, where the temperatures take on significant anti-cross-correlations on inter-seasonal scale, but no significant correlations on inter-annual scale. By analyzing these different spatial patterns, we can better understand the influencing climatological processes of different scales. Therefore, DCCA are recommended as a reliable method in detecting the relations between two climatological variables, and further be useful for our understanding of the whole climate system.

Autocorrelation and cross-correlation in time series of homicide and attempted homicide

We propose in this paper to establish the relationship between homicides and attempted homicides by a non-stationary time-series analysis. This analysis will be carried out by Detrended Fluctuation Analysis (DFA), Detrended Cross-Correlation Analysis (DCCA), and DCCA cross-correlation coefficient, ρDCCA(n). Through this analysis we can identify a positive cross-correlation between homicides and attempted homicides. At the same time, looked at from the point of view of autocorrelation (DFA), this analysis can be more informative depending on time scale. For short scale (days), we cannot identify auto-correlations, on the scale of weeks DFA presents anti-persistent behavior, and for long time scales (n>90 days) DFA presents a persistent behavior. Finally, the application of this new type of statistical analysis proved to be efficient and, in this sense, this paper can contribute to a more accurate descriptive statistics of crime.

Cross-Correlations between Energy and Emissions Markets: New Evidence from Fractal and Multifractal Analysis

We supply a new perspective to describe and understand the behavior of cross-correlations between energy and emissions markets. Namely, we investigate cross-correlations between oil and gas (Oil-Gas), oil and CO2(Oil-CO2), and gas andCO2(Gas-CO2) based on fractal and multifractal analysis. We focus our study on returns of the oil, gas, andCO2during the period of April 22, 2005–April 30, 2013. In the empirical analysis, by using the detrended cross-correlation analysis (DCCA) method, we find that cross-correlations for Oil-Gas, Oil-CO2, and Gas-CO2obey a power-law and are weakly persistent. Then, we adopt the method of DCCA cross-correlation coefficient to quantify cross-correlations between energy and emissions markets. The results show that their cross-correlations are diverse at different time scales. Next, based on the multifractal DCCA method, we find that cross-correlated markets have the nonlinear and multifractal nature and that the multifractality strength for three cross-correlated markets is arranged in the order of Gas-CO2 > Oil-Gas > Oil-CO2. Finally, by employing the rolling windows method, which can be used to investigate time-varying cross-correlation scaling exponents, we analyze short-term and long-term market dynamics and find that the recent global financial crisis has a notable influence on short-term and long-term market dynamics.

Features of the detrended cross-correlation analysis in the time series between absorbable particulate matter and meteorological factors

We simulate and analyze the temporal variation characteristics of PM10, which are particles with an aerodynamic diameter of less than 10 microns, and meteorological factors (temperature, humidity, and wind speed) in eight cities on the Korean peninsula. We employ the detrended cross-correlation analysis (DCCA) method to extract the overall tendency of the hourly variation. The relationships between the PM10 density and meteorological factors are established by using cross-correlation coefficients. As a result of non-Asian dust events, we ascertain from weekly intervals that Andong has the largest value, while Mokpo has the smallest one, in the case of the DCCA cross-correlation coefficient between the PM10 and the temperature. Particularly, the cross-correlations can be compared in eight cities, after we examine whether the cross-correlation would be statistically significant from the random number and the shuffled time series surrogations.

Dynamical analyses of the time series for the temperature and the humidity

We use a detrended cross-correlation analysis (DCCA) method to investigate the dynamical behaviors of the time series for the temperature and the humidity. With our model, we calculate the cross-correlation coefficient between changes in the times series for the temperature and the humidity. Our simulation is performed for and restricted to eight cities around the Korean peninsula. Particularly, for week intervals, the DCCA cross-correlation coefficient shows the largest positive value for Sokcho while it shows the largest negative value for Gangrung. Particularly, the results are compared to those between different international cities.

Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket

We investigate the cross-correlations between Renminbi (CNY) and four major currencies (USD, EUR, JPY, and KRW) in the Renminbi currency basket, i.e., the cross-correlations of CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW. Qualitatively, using a statistical test in analogy to the Ljung-Box test, we find that cross-correlations significantly exist in CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW. Quantitatively, employing the detrended cross-correlation analysis (DCCA) method, we find that the cross-correlations of CNY–USD, CNY–EUR, CNY–JPY, and CNY–KRW are weakly persistent. We use the DCCA cross-correlation coefficient ρDCCA to quantify the level of cross-correlations and find the currency weight in the Renminbi currency basket is arranged in the order of USD>EUR>JPY >KRW. Using the method of rolling windows, which can capture the time-varying cross-correlation scaling exponents, we find that: (i) CNY and USD are positively cross-correlated over time, but the cross-correlations of CNY–USD are anti-persistent during the US sub-prime crisis and the European debt crisis. (ii) The cross-correlation scaling exponents of CNY-EUR have the cyclical fluctuation with a nearly two-year cycle. (iii) CNY–JPY has long-term negative cross-correlations, during the European debt crisis, but CNY and KRW are positively cross-correlated.