The volatility in financial time series based on granule complex network

The volatility is one of the essential characteristics of financial time series, which is vital for the knowledge acquisition from financial data. However, since the high noise and nonsteady features, the volatility identification of financial time series is still a challenging problem. In this paper, from a perspective of granule complex network, a novel approach is proposed to study this problem. First, numeric time series is structured into fuzzy information granules (FIGs), where the segments of time series in each granule would own similar volatility features. Second, by using the transfer relations among granules, granule complex network is to be constructed, which intuitively describes the transfer processes among the different volatility patterns. Third, a novel community detection algorithm is applied to divide the granule complex networks, where granules with frequent mutual transfers would belong to the same granule community. Finally, Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities, which would further describe the larger-scale transitions of volatility in overall financial time series. An empirical study of the proposed system is applied in the Shanghai stock index market, where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities.