POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN CHINESE STOCK MARKETS

2010 ◽  
Vol 09 (02) ◽  
pp. 203-217 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
YULEI PANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Extreme Events ◽  
Stock Markets ◽  
Cross Correlation ◽  
Extreme Values ◽  
Cumulative Distribution ◽  
Stretched Exponential ◽  
Cross Correlation Analysis ◽  
Chinese Stock Markets

This paper reports the statistics of extreme values and positions of extreme events in Chinese stock markets. An extreme event is defined as the event exceeding a certain threshold of normalized logarithmic return. Extreme values follow a piecewise function or a power law distribution determined by the threshold due to a crossover. Extreme positions are studied by return intervals of extreme events, and it is found that return intervals yield a stretched exponential function. According to correlation analysis, extreme values and return intervals are weakly correlated and the correlation decreases with increasing threshold. No long-term cross-correlation exists by using the detrended cross-correlation analysis (DCCA) method. We successfully introduce a modification specific to the correlation and derive the joint cumulative distribution of extreme values and return intervals at 95% confidence level.

MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS OF CHINESE STOCK MARKETS BASED ON TIME DELAY

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 329-338 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
QIUYUE JIN
Keyword(s):  
Time Delay ◽  
Correlation Analysis ◽  
Long Range ◽  
Power Law ◽  
Spectrum Analysis ◽  
Cross Correlation ◽  
Analysis Time ◽  
Singularity Spectrum ◽  
Stock Indices ◽  
Cross Correlation Analysis

Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of two simultaneous series. However, the synchronization of underlying data can not be guaranteed integrated by a variety of factors. We artificially imbed a time delay in considered series and study its influence on the multifractal cross-correlation analysis. Time delay is found to affect the multifractal characterization, where a larger time delay causes a weaker multifractality. We also propose an alternative modification on MF-DXA to make the process more robust. The logarithmic return and volatility of Chinese stock indices show cross-correlation scaling behavior and strong multifractality by MF-DXA as well as singularity spectrum analysis.

MULTISCALE DETRENDED CROSS-CORRELATION ANALYSIS OF STOCK MARKETS

Fractals ◽  
2014 ◽  
Vol 22 (04) ◽  
pp. 1450007 ◽  
Author(s):  
YI YIN ◽  
PENGJIAN SHANG
Keyword(s):  
Correlation Analysis ◽  
Stock Markets ◽  
Cross Correlation ◽  
Statistical Characteristics ◽  
Detailed Knowledge ◽  
Stock Indices ◽  
Regional Markets ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
The Cross

In this paper, we employ the detrended cross-correlation analysis (DCCA) to investigate the cross-correlations between different stock markets. We report the results of cross-correlated behaviors in US, Chinese and European stock markets in period 1997–2012 by using DCCA method. The DCCA shows the cross-correlated behaviors of intra-regional and inter-regional stock markets in the short and long term which display the similarities and differences of cross-correlated behaviors simply and roughly and the persistence of cross-correlated behaviors of fluctuations. Then, because of the limitation and inapplicability of DCCA method, we propose multiscale detrended cross-correlation analysis (MSDCCA) method to avoid "a priori" selecting the ranges of scales over which two coefficients of the classical DCCA method are identified, and employ MSDCCA to reanalyze these cross-correlations to exhibit some important details such as the existence and position of minimum, maximum and bimodal distribution which are lost if the scale structure is described by two coefficients only and essential differences and similarities in the scale structures of cross-correlation of intra-regional and inter-regional markets. More statistical characteristics of cross-correlation obtained by MSDCCA method help us to understand how two different stock markets influence each other and to analyze the influence from thus two inter-regional markets on the cross-correlation in detail, thus we get a richer and more detailed knowledge of the complex evolutions of dynamics of the cross-correlations between stock markets. The application of MSDCCA is important to promote our understanding of the internal mechanisms and structures of financial markets and helps to forecast the stock indices based on our current results demonstrated the cross-correlations between stock indices. We also discuss the MSDCCA methods of secant rolling window with different sizes and, lastly, provide some relevant implications and issue.

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