High noise and strong volatility are the typical characteristics of financial time series. Combined with pseudo-randomness, nonsteady and self-similarity exhibiting in different time scales, it is a challenging issue for the pattern analysis of financial time series. Different from the existing works, in this paper, financial time series are converted into granular complex networks, based on which the structure and dynamics of network models are revealed. By using variable-length division, an extended polar fuzzy information granule (FIGs) method is used to construct granular complex networks from financial time series. Considering the temporal characteristics of sequential data, static networks and temporal networks are studied, respectively. As to the static network model, some features of topological structures of granular complex networks, such as distribution, clustering and betweenness centrality are discussed. Besides, by using the Markov chain model, the transfer processes among different granules are investigated, where the fluctuation pattern of data in the coming step can be evaluated from the transfer probability of two consecutive granules. Shanghai composite index and foreign exchange data as two examples in real life are applied to carry out the related discussion.

中文翻译：

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金融时间序列衍生的粒状复杂网络的结构和动力学

高噪声、强波动性是金融时间序列的典型特征。结合在不同时间尺度上表现出的伪随机性、非定常性和自相似性，金融时间序列的模式分析是一个具有挑战性的问题。与现有工作不同，本文将金融时间序列转化为粒状复杂网络，在此基础上揭示了网络模型的结构和动态。通过使用可变长度划分，使用扩展的极性模糊信息粒（FIGs）方法从金融时间序列构建粒状复杂网络。考虑到序列数据的时间特性，分别研究了静态网络和时间网络。对于静态网络模型，粒状复杂网络拓扑结构的一些特征，讨论了分布、聚类和中介中心性等问题。此外，利用马尔可夫链模型，研究了不同颗粒之间的转移过程，可以从两个连续颗粒的转移概率来评估下一步骤中数据的波动模式。以上证综指和外汇数据作为现实生活中的两个例子进行了相关讨论。