Pengjian Shang

MULTIFRACTAL CROSS-CORRELATION ANALYSIS BASED ON STATISTICAL MOMENTS

We introduce a new method, multifractal cross-correlation analysis based on statistical moments (MFSMXA), to investigate the long-term cross-correlations and cross-multifractality between time series generated from complex system. Efficiency of this method is shown on multifractal series, comparing with the well-known multifractal detrended cross-correlation analysis (MFXDFA) and multifractal detrending moving average cross-correlation analysis (MFXDMA). We further apply this method on volatility time series of DJIA and NASDAQ indices, and find some interesting results. The MFSMXA has comparative performance with MFXDMA and sometimes perform slightly better than MFXDFA. Multifractal nature exists in volatility series. In addition, we find that the cross-multifractality of volatility series is mainly due to their cross-correlations, via comparing the MFSMXA results for original series with those for shuffled series.

MULTISCALE ENTROPY ANALYSIS OF TRAFFIC TIME SERIES

There has been considerable interest in quantifying the complexity of different time series, such as physiologic time series, traffic time series. However, these traditional approaches fail to account for the multiple time scales inherent in time series, which have yielded contradictory findings when applied to real-world datasets. Then multi-scale entropy analysis (MSE) is introduced to solve this problem which has been widely used for physiologic time series. In this paper, we first apply the MSE method to different correlated series and obtain an interesting relationship between complexity and Hurst exponent. A modified MSE method called multiscale permutation entropy analysis (MSPE) is then introduced, which replaces the sample entropy (SampEn) with permutation entropy (PE) when measuring entropy for coarse-grained series. We employ the traditional MSE method and MSPE method to investigate complexities of different traffic series, and obtain that the complexity of weekend traffic time series differs from that of the workday time series, which helps to classify the series when making predictions.

Weighted multifractal cross-correlation analysis based on Shannon entropy

Abstract In this paper, we propose a modification of multifractal cross-correlation analysis based on statistical moments (MFSMXA) method, called weighted MFSMXA method based on Shannon entropy (W-MFSMXA), to investigate cross-correlations and cross-multifractality between time series. Robustness of this method is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed W-MFSMXA method not only keep the multifractal structure unchanged, but contains more significant information of series compared to the previous MFSMXA method. Furthermore, analytic formulas of the binomial multifractal model are generated for W-MFSMXA. Theoretical analysis and finite-size effect test demonstrate that W-MFSMXA slightly outperforms MFSMXA for relatively shorter series. We further generate the scaling exponent ratio to describe the relation of two methods, whose profile is found approximating a centrosymmetric hyperbola. Cross-multifractality is found in returns series but then destroyed after being shuffled as a consequence of the removed long memory in separate series.

EFFECT OF LINEAR AND NONLINEAR FILTERS ON MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS

When probing the dynamical properties of complex systems, such as physical and physiological systems, the output signal may be not the expected one. It is often a linear or nonlinear filter (or a transformation) of the right one represented the properties we want to investigate. Besides, for a multiple-component system, it is necessary to consider the relations between different influence factors. Here, we investigate what effect kinds of linear and nonlinear filters have on the cross-correlation properties of monofractal series and binomial multifractal series relatively. We use the multifractal detrended cross-correlation analysis (MFDCCA) that has been known well for its accurate quantization of cross-correlations between two time series. We study the effect of five filters: (i) linear (yi = axi + b); (ii) polynomial ; (iii) logarithmic (yi = log(xi + δ)); (iv) exponential (yi = exp(axi + b)); and (v) power-law (yi = (xi + a)b). We find that for both monofractal and multifractal signals, linear filters have no effect on the cross-correlation properties while the influence of polynomial, logarithmic and power-law filters mainly depends on (a) the strength of cross-correlations in the original series; (b) the parameter b of the polynomial filter; (c) the offset δ in the logarithmic filter; and (d) both the parameter a and b of the power-law filter. In addition, the parameter a and b of the exponential filter change the cross-correlation properties of monofractal signal, yet they have little influence on that of multifractal signal.

MULTISCALE ENTROPY ANALYSIS OF FINANCIAL TIME SERIES

The paper mainly applies the multiscale entropy (MSE) to analyze the financial time series. The MSE is used to examine the complexity of a quantified system. Based on MSE, we propose multiscale cross-sample entropy (MSCE) to analyze the complexity and correlation of two time series. By comparing with the results, we find that both results present remarkable scaling characterization and the value of each log return of financial time series decreases with a increasing scale factor. From the results of MSE, we also find that the entropy of the Europe markets is lower than that of the Asia, but higher than that of the Americas. It means the MSE can distinguish different areas markets. The results of MSCE show that financial plate have high synchrony with the plate of Electron, IT and Realty. The MSCE can distinguish the highly synchronous plates.

POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN 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.

Fractal nature of highway traffic data

In this paper, we applied a fractal approach to analyze the traffic data collected from the Beijing Yuquanying. The power spectrum, the empirical probability distribution function, the statistical moment scaling function and the autocorrelation function are used as indicators to investigate the presence of the fractal. The results from the fractal identification methods indicate that these data exhibit fractal behavior. A fractal framework seemed well suited for description of the data observed here, but its suitability for general traffic systems was not clear.

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

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.

Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series

We use detrended fluctuation analysis (DFA) method to detect the long-range correlation and scaling properties of daily precipitation series of Beijing from 1973 to 2004 before and after adding diverse trends to the original series. The correlation and scaling properties of the original series are difficult to analyze due to existing crossovers. The effects of the coefficient and the power of the added trends on the scaling exponents and crossovers of the series are tested. A crossover is found to be independent of the added trends, which arises from the intrinsic periodic trend of the precipitation series. However, another crossover caused by the multifractal vanishes with the increasing power of added trends.

Permutation complexity and dependence measures of time series

It is an interesting area to analyze the complexity or dependence of time series. Many information-theoretic methods have been proposed for this purpose. In this letter, we adapt the permutation entropy to infer the complexity of short-time series by freely changing the time delay, and test it with Gaussian random series and random walks. We also propose a Renyi permutation entropy to characterize the rare events from frequent events. It successfully analyzes the temporal structure of the autoregressive (AR) model and also the daily closing prices in Shanghai stock market. Moreover, we introduce a permutation mutual information method to detect the dependence between two time series. We test it by the Henon map, autoregressive fractionally integrated moving average (ARFIMA) model and observe its significance by the randomization test. It is also applied to measure the dependence between air temperature and air humidity.