基于复杂网络的时间序列双变量相关性波动研究

Research on fluctuation of bivariate correlation of time series based on complex networks theory

为了研究具有时间序列特征的双变量之间相关性的波动规律,本文选取国际原油期货价格和中国大庆原油现货价格作为样本数据,借鉴统计物理学的方法进行研究.运用粗粒化方法建立了相关性波动模态,并利用复杂网络理论和分析方法对双变量相关性波动模态的统计、变化规律及其演化机理三个问题进行了分析.结果显示,双变量相关性波动模态分布具有幂律性、群簇性和周期性,相关性波动主要通过少数几种模态进行传递和演化.这些研究成果不仅可以作为双变量间相关性波动研究的方法,也为不同变量间相关性波动一般规律的研究提供了思路.

In order to study the fluctuation of bivariate correlation which had time series characters, this paper selected International crude oil futures prices and Chinese Daqing crude oil spot prices as the sample data, using the method of statistical physics to study. The modes of fluctuation of correlation were defined by coarse graining process. Then three problems modes＇ statistics, law of variation and evolution mechanism were analyzed by complex network theory and analytical method. The results indicated that forms of modes showed that consecutive days of weak or strong positive correlation, and modes obeyed the power-law distribution. There were three kinds of sub- groups appearing in the network of fluctuation of bivariate correlation. These sub-groups were fluctuation of weak positive correlation, strong positive correlation and unrelated, and a core mode existed in each category of sub-groups. Transmission and evolution of fluctuation of bivariate correlation were a few modes. The fluctuation of bivariate correlation was transmitted and evolved by a few modes. The fluctuation had periodicity that the transmission among modes need average 8.74 days and a whole volatility cycle need about 18.55 days. These results not only can be the analyze method between two variables but also provides idea for researching a general law in different variables.