Compositional segmentation of time series in the financial markets

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.