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Abstract: Time irreversibility is a fundamental property of many time series. We apply the multiscale entropy (MSE) and multiscale time irreversibility (MSTI) to analyze the financial time series, and succeed to classify the financial markets. Interestingly, both methods have nearly the same classification results, which mean that they are capable of distinguishing different series in a reliable manner. By comparing the results of shuffled data with the original results, we confirm that the asymmetry property is an inherent property of financial time series and it can extend over a wide range of scales. In addition, the effect of noise on Americas markets and Europe markets are relatively more significant than the effect on Asia markets, and loss of time irreversibility has been detected in high noise added series. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, we analyze time series on the basis of the visibility graph algorithm that maps the original series into a graph. By taking into account the all-round information carried by the signals, the time irreversibility and fractal behavior of series are evaluated from a complex network perspective, and considered signals are further classified from different aspects. The reliability of the proposed analysis is supported by numerical simulations on synthesized uncorrelated random noise, short-term correlated chaotic systems and long-term correlated fractal processes, and by the empirical analysis on daily closing prices of eleven worldwide stock indices. Obtained results suggest that finite size has a significant effect on the evaluation, and that there might be no direct relation between the time irreversibility and long-range correlation of series. Similarity and dissimilarity between stock indices are also indicated from respective regional and global perspectives, showing the existence of multiple features of underlying systems. [ABSTRACT FROM AUTHOR]

Many information-theoretic methods have been proposed for analyzing the coupling dependence between time series. And it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system. Recently, we developed a new permutation-based entropy, called cross-permutation entropy (CPE), to detect the coupling structures between two synchronous time series. In this paper, we extend the CPE method to weighted cross-permutation entropy (WCPE), to address some of CPE’s limitations, mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor. It shows more stable and reliable results than CPE does when applied it to spiky data and AR(1) processes. Besides, we adapt the CPE method to infer the complexity of short-length time series by freely changing the time delay, and test it with Gaussian random series and random walks. The modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one. Finally, the weighted cross-permutation entropy of eight important stock indices from the world financial markets is investigated, and some useful and interesting empirical results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a complexity measure based on the entropic segmentation called sequence compositional complexity ( S C C ) into the analysis of financial time series. S C C was first used to deal directly with the complex heterogeneity in nonstationary DNA sequences. We already know that S C C was found to be higher in sequences with long-range correlation than those with low long-range correlation, especially in the DNA sequences. Now, we introduce this method into financial index data, subsequently, we find that the values of S C C of some mature stock indices, such as S & P 500 (simplified with S & P in the following) and H S I , are likely to be lower than the S C C value of Chinese index data (such as S S E ). What is more, we find that, if we classify the indices with the method of S C C , the financial market of Hong Kong has more similarities with mature foreign markets than Chinese ones. So we believe that a good correspondence is found between the S C C of the index sequence and the complexity of the market involved. [ABSTRACT FROM AUTHOR]

We introduce an entropic segmentation algorithm and apply it to decompose the financial sequences into compositionally homogeneous domains. To probe more about the nature of the financial time series, we investigate the statistical properties of the segment from the view of segmentation position and segment length first. We reveal some important and interesting conclusions and information hidden in these time series of stock markets. Then, we focus on the study of the intrinsic properties for each segment in the time series from two aspects: time irreversibility and correlation. The fluctuations on the time irreversibility and the scaling exponent all support that the segments present compositional heterogeneity and verify the segmentation. Meanwhile, we conclude that time irreversibility is inherent in the stock time series and verifies that stock markets are nonequilibrium systems essentially even though segmentation. Moreover, the scaling exponents for each segment point out that the traditional detrended fluctuation analysis is not applicable to measure the correlation for the whole original time series of stock market. [ABSTRACT FROM AUTHOR]