基于复杂网络的时间序列单变量波动幅度研究  

RESEARCH ON THE FLUCTUATION RANGE OF SINGLE VARIABLE TIME SERIES BASED ON COMPLEX NETWORKS

作　　者：安海岗[1] 都沁军[1] 张永礼[1] 

机构地区：[1]石家庄经济学院,石家庄050031

出　　处：《系统科学与数学》2015年第2期158-169,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目"基于复杂网络的虚拟社区关系挖掘与网络舆情演化分析"(71173199);国土资源部资源环境承载力评价重点实验室;河北省高校重点学科建设项目;河北省教育厅重点项目(SD14048);河北省科技厅项目(13210339);校内博士基金项目联合资助课题

摘　　要：为研究时间序列单变量波动幅度演变规律,文章选择伦敦金下午收盘价格作为样本数据,借鉴统计物理学的方法进行研究.利用粗粒化方法建立了价格波动幅度变化模态,运用复杂网络理论对时间序列单变量波动幅度模态的统计、变化规律和演化规律进行了分析.研究结果表明,时间序列单变量波动幅度模态分布具有幂律性、群簇性和周期性,其波动幅度模态主要通过少数几种模态进行转换与演化.本研究方法不仅可以对不同类型时间序列单变量波动幅度进行研究,同时可为多变量波动幅度及其联动波动规律研究提供思路.In order to study the evolution law of the fluctuation range of single variable time series, this article chose closing price in the afternoon of London Gold from January 1, 2002 to February 28, 2014 as the sample data, in refer to the method of statistical physics research. Using Parkinson＇s definition about fluctuation range,it defines the calculation method of single variable fluctuation range, and uses coarse- grained method to transform price fluctuation range into symbolic sequences consisted of three characters {H, M, L}. The nodes of the fluctuation range complex network are 5-symbol strings in the form of data window linked in the network＇s topology by sliding sequence. The single variable fluctuation range complex network is composed of 149 models and the link edges between them. The former 32 nodes account for 79% of the strength degree distribution. It does not show a good correlation between weighted clustering coefficient and point of strength. There are 10 small clusters that contain 8 points and above it in the network. The average shortest path length of network is 6.561, which means the price fluctuation range has periodicity. Some points that have higher degree have weaker betweenness centrality, however, some other points that have lower degree have an important role in the route of the network. In summary, the paper used the complex network theory to analyze the statistics, variation and evolution regularity of single variable time series fluctuation range mode. The result shows that the single variable time series fluctuation range has the characteristic of power-law,clustering and periodicity, and its fluctuation range models mainly apply a handful of models to transfer and evolve. The research results in this paper can not only provide methods for different types of single variable time series fluctuation range research, but also provide ideas for multiple variables fluctuation range and its linkage variation rule research.

关 键 词：复杂网络 时间序列 波动幅度 粗粒化 

分 类 号：O157.5[理学—数学] O211.61[理学—基础数学]