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

Gao Xiang-Yun An Hai-Zhong Fang Wei

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

Gao Xiang-Yun, An Hai-Zhong, Fang Wei
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  • 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.
      Corresponding author: , ahz369@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 71173199), the Humanities and Social Sciences Planning Funds Project under the Ministry of Education of the PRC (Grant No. 10YJA630001) and The Fundamental Research Funds for the Central Universities (Grant No.2011PY0215).
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    Coppola A 2008 J. Futures Mark. 28 34

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    Wackerbauer R, Witt A, Atmanspacher H, Kurths J, Scheingraber H 1994 Chaos Solitons Fractals 4 133

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    Feng G L, Hou W, Dong W J 2006 Acta Phys. Sin. 55 962 (in Chinese) [封国林, 侯威, 董文杰 2006 物理学报 55 962]

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    Xu P J, Tang Y Y, Zhang J, Zhang Z B, Wang K, Shao Y, Shen H J, Mao Y C 2011 Acta Phys. Chim. Sin. 27 1839 (in Chinese) [许佩军, 唐媛媛, 张静, 张知博, 王昆, 邵颖, 沈虎峻, 毛英臣 2011物理化学学报 27 1839]

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    Zhang H Y, Wang Y Y, Tao G Q, Gui B, Yin C L, Chai Y M, Que G H 2011 Acta Chim. Sin. 69 2053 (in Chinese) [张宏玉, 王艳艳, 陶国强, 桂彬, 殷长龙, 柴永明 2011 化学学报 69 2053]

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    Watts D J, Strogatz S H 1998 Nature 393 6684

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    Newman M E J 1999 Phys. Lett. A 263 341

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    Barabási A L, Albert R 1999 Science 286 509

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    Janssen M A, Walker B H, Langridge J, Abel N 2000 Ecol. Modell. 131 249

    [17]

    Zhang L, Liu Y 2008 Acta Phy. Sin. 57 5419 (in Chinese) [张立, 刘云 2008 物理学报 57 5419]

    [18]

    Kelesa A, Kolcakb M, Keles A 2008 Knowl. Based Syst. 21 951

    [19]

    Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) [周磊, 龚志强, 支蓉, 封国林 2008 物理学报 57 7380]

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    Chen W D, Xu H, Guo Q 2010 Acta Phys. Sin. 59 4514 (in Chinese) [陈卫东, 徐华, 郭琦 2010 物理学报 59 4514]

    [21]

    Gao X Y, An H Z, Liu H H, Ding Y H 2011 Acta Phy.sin.60 0689021 (in Chinese) [高湘昀, 安海忠, 刘红红, 丁颖辉 2010 物理学报 60 0689021]

    [22]

    Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835

    [23]

    Wasserman S, Faust K 1994 Social network analysis: Methods and applications (Cambridge: Cambridge University Press) p275

    [24]

    Ronald S B 1992 Strnctural Holes: the Social Strulture of Competition (Cambridge: Harvard University Press) p66

    [25]

    Barrat A, Barthelemy M, Pastor S R, Vespignani A, 2004 Proc. Nalt. Acad. Sci. U.S.A 101 3747

  • [1]

    James E H, Davidson, David F H, Frank S, Yeo S 1978 Econ. J. 88 661

    [2]

    Robert F E, Granger C W J 1987 Econometrica 55 251

    [3]

    Nathan S B, Thomas B F 1997 Int. Econ. Rev. 38 627

    [4]

    Coppola A 2008 J. Futures Mark. 28 34

    [5]

    Svetlana M, Russell S 2009 Energ Policy 37 1687

    [6]

    Huang B N, Yang C W, Hwang M J 2009 Energy Econ. 31 91

    [7]

    Hao B L 1999 Science 51 3

    [8]

    Wackerbauer R, Witt A, Atmanspacher H, Kurths J, Scheingraber H 1994 Chaos Solitons Fractals 4 133

    [9]

    Feng G L, Hou W, Dong W J 2006 Acta Phys. Sin. 55 962 (in Chinese) [封国林, 侯威, 董文杰 2006 物理学报 55 962]

    [10]

    Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中2007 物理学报 56 3152]

    [11]

    Xu P J, Tang Y Y, Zhang J, Zhang Z B, Wang K, Shao Y, Shen H J, Mao Y C 2011 Acta Phys. Chim. Sin. 27 1839 (in Chinese) [许佩军, 唐媛媛, 张静, 张知博, 王昆, 邵颖, 沈虎峻, 毛英臣 2011物理化学学报 27 1839]

    [12]

    Zhang H Y, Wang Y Y, Tao G Q, Gui B, Yin C L, Chai Y M, Que G H 2011 Acta Chim. Sin. 69 2053 (in Chinese) [张宏玉, 王艳艳, 陶国强, 桂彬, 殷长龙, 柴永明 2011 化学学报 69 2053]

    [13]

    Watts D J, Strogatz S H 1998 Nature 393 6684

    [14]

    Newman M E J 1999 Phys. Lett. A 263 341

    [15]

    Barabási A L, Albert R 1999 Science 286 509

    [16]

    Janssen M A, Walker B H, Langridge J, Abel N 2000 Ecol. Modell. 131 249

    [17]

    Zhang L, Liu Y 2008 Acta Phy. Sin. 57 5419 (in Chinese) [张立, 刘云 2008 物理学报 57 5419]

    [18]

    Kelesa A, Kolcakb M, Keles A 2008 Knowl. Based Syst. 21 951

    [19]

    Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese) [周磊, 龚志强, 支蓉, 封国林 2008 物理学报 57 7380]

    [20]

    Chen W D, Xu H, Guo Q 2010 Acta Phys. Sin. 59 4514 (in Chinese) [陈卫东, 徐华, 郭琦 2010 物理学报 59 4514]

    [21]

    Gao X Y, An H Z, Liu H H, Ding Y H 2011 Acta Phy.sin.60 0689021 (in Chinese) [高湘昀, 安海忠, 刘红红, 丁颖辉 2010 物理学报 60 0689021]

    [22]

    Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835

    [23]

    Wasserman S, Faust K 1994 Social network analysis: Methods and applications (Cambridge: Cambridge University Press) p275

    [24]

    Ronald S B 1992 Strnctural Holes: the Social Strulture of Competition (Cambridge: Harvard University Press) p66

    [25]

    Barrat A, Barthelemy M, Pastor S R, Vespignani A, 2004 Proc. Nalt. Acad. Sci. U.S.A 101 3747

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  • Received Date:  13 January 2012
  • Accepted Date:  10 May 2012
  • Published Online:  05 May 2012

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

    Corresponding author: ahz369@163.com
  • 1. Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China;
  • 2. School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 71173199), the Humanities and Social Sciences Planning Funds Project under the Ministry of Education of the PRC (Grant No. 10YJA630001) and The Fundamental Research Funds for the Central Universities (Grant No.2011PY0215).

Abstract: 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.

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