scholarly journals Multifractal temporally weighted detrended partial cross-correlation analysis of two non-stationary time series affected by common external factors

2021 ◽  
pp. 125920
Author(s):  
Bao-Gen Li ◽  
Dian-Yi Ling ◽  
Zu-Guo Yu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Cross Correlation ◽  
External Factors ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Cross Correlation Analysis

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.

Importance of Body Sway Velocity Information in Controlling Ankle Extensor Activities During Quiet Stance

2003 ◽  
Vol 90 (6) ◽  
pp. 3774-3782 ◽  
Author(s):  
Kei Masani ◽  
Milos R. Popovic ◽  
Kimitaka Nakazawa ◽  
Motoki Kouzaki ◽  
Daichi Nozaki
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Muscle Activity ◽  
Cross Correlation ◽  
Gastrocnemius Muscle ◽  
Quiet Stance ◽  
Lateral Gastrocnemius ◽  
Velocity Feedback ◽  
Cross Correlation Analysis ◽  
Velocity Information

In literature, it has been suggested that the CNS anticipates spontaneous change in body position during quiet stance and continuously modulates ankle extensor muscle activity to compensate for the change. The purpose of this study was to investigate whether velocity feedback contributes by modulating ankle extensor activities in an anticipatory fashion, facilitating effective control of quiet stance. Both theoretical analysis and experiments were carried out to investigate to what extent velocity feedback contributes to controlling quiet stance. The experiments were carried out with 16 healthy subjects who were asked to stand quietly with their eyes open or closed. During the experiments, the center of pressure (COP) displacement (COPdis), the center of mass (COM) displacement (COMdis), and COM velocity (COMvel) in the anteroposterior direction were measured. Rectified electromyograms (EMGs) were used to measure muscle activity in the right soleus muscle, the medial gastrocnemius muscle, and the lateral gastrocnemius muscle. The simulations were performed using an inverted pendulum model that described the anteroposterior kinematics and dynamics of quiet stance. In the simulations, an assumption was made that the COMdis of the body would be regulated using a proportional-derivative (PD) controller. Two different PD controllers were evaluated in these simulations: 1) a controller with the high-derivative/velocity gain (HDG) and 2) a controller with the low-derivative/velocity gain (LDG). Cross-correlation analysis was applied to investigate the relationships between time series obtained in experiments 1) COMdis and EMGs and 2) COMvel and EMGs. Identical cross-correlation analysis was applied to investigate the relationships between time series obtained in simulations 3) COMdis and ankle torque and 4) COMvel and ankle torque. The results of these analyses showed that the COMdis was positively correlated with all three EMGs and that the EMGs temporally preceded the COMdis. These findings agree with the previously published studies in which it was shown that the lateral gastrocnemius muscle is actively modulated in anticipation of the body's COM position change. The COMvel and all three EMGs were also correlated and the cross-correlation function (CCF) had two peaks: one that was positive and another that was negative. The positive peaks were statistically significant, unlike the negative ones; they were larger than the negative peaks; and their time shifts were much shorter compared with the time shifts of the negative peaks. When these results were compared with the CCF results obtained for simulated time series, it was discovered that the cross-correlation results for the HDG controller closely matched cross-correlation results for the experimental time series. On the other hand, the simulation result obtained for LDG controller did not match the experimental results. These findings suggest that the actual postural control system during quiet stance adopts a control strategy that relies notably on velocity information and that such a controller can modulate muscle activity in anticipatory manner without using a feed-forward mechanism.

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