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A new method is proposed in this paper—moving cut data-rescaled range analysis (MC-R/S). Tests on the correlated time series suggest that the MC-R/S can accurately detect the time-instants of abrupt change, and the MC-R/S results almost do not depend on the length of subseries and are less affected by noises. So, MC-R/S is suitable to detecting an abrupt dynamic change in those time series exhibiting correlations, and can very well make up the deficiency of moving detrended fluctuation analysis (MDFA).
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Keywords:
- scaling exponent /
- moving cut data-rescaled range analysis /
- moving detrended fluctuation analysis /
- abrupt dynamic change
[1] Fu C B, Wang Q 1992 Chin. J. Atmos. Sci. 16 483 (in Chinese) [符淙斌、王 强 1992 大气科学16,483]
[2] Mandelbrot B B 1967 Sci. 156 636
[3] He W P 2008 The research and application of the abrupt detecting methods in dynamical structures (Lanzhou: Lanzhou University) p16 (in Chinese)[何文平 2008 动力学结构突变检测方法的研究及其应用(第16页)]
[4] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geo. 15 601
[5] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese)[何文平、吴 琼、张 文、王启光、张 勇 2009 58 2862]
[6] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[7] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[8] Dai X G, Fu C B, Wang P 2005 Chin. Phys. 14 850
[9] Dai X G, Wang P, Chou J F 2004 Pro. in Chin. Sci. 60 544
[10] Liu S D, Chen J, Liu S K 1999 J. Appl. Meteor. Sci. (supplement) 10 10 (in Chinese)[刘式达、陈 炯、刘式适 1999 应用气象学报(增刊)10 10]
[11] Liu S D, Rong P P, Chen J 2000 Acta Meteor. Sin. 58 111 (in Chinese)[刘式达、荣平平、陈 炯 2000 气象学报 58 111]
[12] Cao H X, Zheng Z F, Zhang X L, Xie X L, Pan J H 2007 Chin. J. Geo. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华 2007 地球 50 420]
[13] Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[14] Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
[15] Bunde A, Havlin S, Kantelhardt J W, Penzel T T, Peter J H, Voigt K 2000 Phys. Rev. Lett. 85 3736
[16] Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[17] Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[18] Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[19] Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[20] He W P 2008 The research and application of the abrupt detecting methods in dynamical structures (Lanzhou: Lanzhou University) p37 (in Chinese) [何文平 2008 动力学结构突变检测方法的研究及其应用(第37页)]
[21] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[22] Feng G L, Dai X G, Wang A H 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧 2001 50 606]
[23] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear theories and methods on spatial-temporal distribution of the observational data (Beijing: Metrological Press) p227 (in Chinese)[封国林、董文杰、龚志强、侯 威、万仕全、支 蓉 2006 观测数据非线性时空分布理论和方法 (北京:气象出版社)第227页]
[24] Carvalho L M V, Tsonis A A, Jones C, Rocha1 H R, Polito P S 2007 Non. Proc. Geo. 14 723
[25] Hurst H E 1951 Trans. Am. Soc. Civ. Eng . 116 770
[26] Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
[27] Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501
[28] May R 1976 Nature 261 459
[29] Mann H B 1945 Econometrica 13 245
[30] Kendall M G, Charles G 1975 Rank Correlation Methods (New York: Oxford University) p202
[31] Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan. 63 1157
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[1] Fu C B, Wang Q 1992 Chin. J. Atmos. Sci. 16 483 (in Chinese) [符淙斌、王 强 1992 大气科学16,483]
[2] Mandelbrot B B 1967 Sci. 156 636
[3] He W P 2008 The research and application of the abrupt detecting methods in dynamical structures (Lanzhou: Lanzhou University) p16 (in Chinese)[何文平 2008 动力学结构突变检测方法的研究及其应用(第16页)]
[4] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geo. 15 601
[5] He W P, Wu Q, Zhang W, Wang Q G, Zhang Y 2009 Acta Phys. Sin. 58 2862 (in Chinese)[何文平、吴 琼、张 文、王启光、张 勇 2009 58 2862]
[6] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[7] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[8] Dai X G, Fu C B, Wang P 2005 Chin. Phys. 14 850
[9] Dai X G, Wang P, Chou J F 2004 Pro. in Chin. Sci. 60 544
[10] Liu S D, Chen J, Liu S K 1999 J. Appl. Meteor. Sci. (supplement) 10 10 (in Chinese)[刘式达、陈 炯、刘式适 1999 应用气象学报(增刊)10 10]
[11] Liu S D, Rong P P, Chen J 2000 Acta Meteor. Sin. 58 111 (in Chinese)[刘式达、荣平平、陈 炯 2000 气象学报 58 111]
[12] Cao H X, Zheng Z F, Zhang X L, Xie X L, Pan J H 2007 Chin. J. Geo. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华 2007 地球 50 420]
[13] Abaimov S G, Turcotte D L, Shcherbakov R, Rundle J B 2007 Non. Proc. Geophys. 14 455
[14] Blender R, Fraedrich K, Sienz F 2008 Non. Proc. Geo. 15 557
[15] Bunde A, Havlin S, Kantelhardt J W, Penzel T T, Peter J H, Voigt K 2000 Phys. Rev. Lett. 85 3736
[16] Bunde A, Eichner J F, Kantelhardt J W, Havlin S 2005 Phys. Rev. Lett. 94 048701
[17] Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[18] Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 8 046133-1
[19] Govindan R B, Vjushin D, Brenner S, Bunde A, Havlin S, Schellnhuber H J 2001 Phys. A 294 239
[20] He W P 2008 The research and application of the abrupt detecting methods in dynamical structures (Lanzhou: Lanzhou University) p37 (in Chinese) [何文平 2008 动力学结构突变检测方法的研究及其应用(第37页)]
[21] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[22] Feng G L, Dai X G, Wang A H 2001 Acta Phys. Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧 2001 50 606]
[23] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear theories and methods on spatial-temporal distribution of the observational data (Beijing: Metrological Press) p227 (in Chinese)[封国林、董文杰、龚志强、侯 威、万仕全、支 蓉 2006 观测数据非线性时空分布理论和方法 (北京:气象出版社)第227页]
[24] Carvalho L M V, Tsonis A A, Jones C, Rocha1 H R, Polito P S 2007 Non. Proc. Geo. 14 723
[25] Hurst H E 1951 Trans. Am. Soc. Civ. Eng . 116 770
[26] Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
[27] Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501
[28] May R 1976 Nature 261 459
[29] Mann H B 1945 Econometrica 13 245
[30] Kendall M G, Charles G 1975 Rank Correlation Methods (New York: Oxford University) p202
[31] Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan. 63 1157
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