Compositional segmentation and complexity measurement in stock indices

In this paper, we introduce a complexity measure based on the entropic segmentation called sequence compositional complexity (SCC) into the analysis of financial time series. SCC was first used to deal directly with the complex heterogeneity in nonstationary DNA sequences. We already know that SCC 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 SCC of some mature stock indices, such as S&P500 (simplified with S&P in the following) and HSI, are likely to be lower than the SCC value of Chinese index data (such as SSE). What is more, we find that, if we classify the indices with the method of SCC, 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 SCC of the index sequence and the complexity of the market involved.