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By combining detrended fluctuation analysis (DFA) method with surrogate data method, and using the Heuristic segmentation algorithm as well as Chi-Square statistics, we develop a new method to determine the threshold of extreme events, e.g. stochastically re-sorting detrended fluctuation analysis (S-DFA) method. The S-DFA method has a certain phsical background, when the occurrence rate of the data is small, then these data belong to little-probability events and they contain so little information about the dynamic system, the states corresponding to these data are abnormal states or extreme states of the system. When the occurrence rate of the data is large or even in distribution these data do not belong to little-probability events and they contain much information about the system, the states corresponding to these data are normal states of the system. Compared with the Percentile curves method, the S-DFA method gives the critical value between extreme event and non-extreame event, which is definite and unique. We also extensively validate the effectiveness of S-DFA method through extreme event detection.
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Keywords:
- detrended fluctuation analysis /
- surrogate data /
- extreme event /
- threshold
[1] IPCC 2001 Climate Change (New York: Cambridge University Press) p155
[2] Soloman S, Qin D H, Manning M, Alley R B, Berntsen T 2007 Climate Chang(New York:Cambridge University Press)p316
[3] [4] Xiong K G, Yang J, Wang S Q, Feng G L, Hu J G 2009 Acta Phys. Sin. 58 2843 (in Chinese) [熊开国、 杨 杰、 万仕全、 封国林、 胡经国 2009 物理学报 58 2843 ]
[5] [6] [7] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Metho-ds on Spatial-Temporal Distribution of the Observational Data (Beijing:Metrological Press) p84 (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)]
[8] Zhang D Q, Yang J, Wang Q G, Feng G L 2009 Acta Phys.Sin. 58 4354 (in Chinese) [章大全、 杨 杰、 王启光、 封国林 2009 物理学报 58 4354]
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[11] [12] Render S, Petersen M R 2006 Phys. Rev. E 74 061114
[13] [14] [15] Zhang D Q, Zhang L, Yang J, Feng G L 2010 Acta Phys. Sin. 59 655 (in Chinese) [章大全、 张 璐、 杨 杰、 封国林 2010 物理学报 59 655]
[16] Yang J, Hou W, Feng G L 2010 Acta Phys. Sin. 59 664 (in Chinese) [杨 杰、 侯 威、 封国林 2010 物理学报 59 664]
[17] [18] [19] Wan S Q, Gu C H, Kang J P 2010 Acta Phys. Sin. 59 676 (in Chinese) [万仕全、 顾承华、 康建鹏等 2010 物理学报 59 676]
[20] Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[21] [22] [23] He W P, Feng GL, Wu Q, Wan S Q, Chou J F 2009 Non. Proc. Geophys. 15 601
[24] Janosi I M,Janecsko B,Kondor I 1999 Physica A 269 111
[25] [26] Ausloos M 2000 Physica A 285 48
[27] [28] [29] Fraedrich K 2002 Stoch. Dynam. 2 403
[30] Lux T, Marehesi M 1999 Nature 397 498
[31] [32] Yang P, Hou W, Feng G L 2008 Acta Phys. Sin. 57 5333 (in Chinese)[杨 萍、 侯 威、 封国林 2008 物理学报 57 5333]
[33] [34] [35] Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[36] Lee J M, Kin D J, Kim I Y 2002 Computers in Biology and Medicine 32 37
[37] [38] [39] Ott E 1993 Chaos in dynamical systems (Cambridge, UK: Cambridge University Press) p305
[40] Theiler J, Linsay P S 1993 M Rubin Time Series Prediction: Forecasting the Future and Understanding the Past (Addison-Wesley, Reading Mass. Press) p429
[41] [42] [43] Timmer J 1998 Phys. Rev. E 58 5153
[44] [45] Theiler J, Eubank S, Longtin A 1992 Physica D 58 77
[46] Kugiumtzis D 2000 Phys. Rev. E 62 25
[47] [48] [49] Timmer J 2000 Phys. Rev. Lett. 85 2647
[50] [51] Stam C J, Mpijn J P, Pritchard W S 1998 Physica D 112 361
[52] Bernaola G P 2001 Phys. Rev. Lett. 87 168
[53] [54] [55] Oliver J L, Bernaola G P, Carpena P, Romn R R 2001 Gene 276 47
[56] Chernoff H, Lehmann E L 1954 The Annals of Mathematical Statistics 25 579
[57] [58] Plackett R L 1993 International Statistical Review 51 59
[59] [60] [61] Greenwood P E, Nikulin M S 1996 Wiley, New York. ISBN 047155779X
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[1] IPCC 2001 Climate Change (New York: Cambridge University Press) p155
[2] Soloman S, Qin D H, Manning M, Alley R B, Berntsen T 2007 Climate Chang(New York:Cambridge University Press)p316
[3] [4] Xiong K G, Yang J, Wang S Q, Feng G L, Hu J G 2009 Acta Phys. Sin. 58 2843 (in Chinese) [熊开国、 杨 杰、 万仕全、 封国林、 胡经国 2009 物理学报 58 2843 ]
[5] [6] [7] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006 Nonlinear Theories and Metho-ds on Spatial-Temporal Distribution of the Observational Data (Beijing:Metrological Press) p84 (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)]
[8] Zhang D Q, Yang J, Wang Q G, Feng G L 2009 Acta Phys.Sin. 58 4354 (in Chinese) [章大全、 杨 杰、 王启光、 封国林 2009 物理学报 58 4354]
[9] [10] Easterling D R, Evans J L, Groisman P Y 2000 Bulletin of the American Meteorological Socie-ty 81 417
[11] [12] Render S, Petersen M R 2006 Phys. Rev. E 74 061114
[13] [14] [15] Zhang D Q, Zhang L, Yang J, Feng G L 2010 Acta Phys. Sin. 59 655 (in Chinese) [章大全、 张 璐、 杨 杰、 封国林 2010 物理学报 59 655]
[16] Yang J, Hou W, Feng G L 2010 Acta Phys. Sin. 59 664 (in Chinese) [杨 杰、 侯 威、 封国林 2010 物理学报 59 664]
[17] [18] [19] Wan S Q, Gu C H, Kang J P 2010 Acta Phys. Sin. 59 676 (in Chinese) [万仕全、 顾承华、 康建鹏等 2010 物理学报 59 676]
[20] Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[21] [22] [23] He W P, Feng GL, Wu Q, Wan S Q, Chou J F 2009 Non. Proc. Geophys. 15 601
[24] Janosi I M,Janecsko B,Kondor I 1999 Physica A 269 111
[25] [26] Ausloos M 2000 Physica A 285 48
[27] [28] [29] Fraedrich K 2002 Stoch. Dynam. 2 403
[30] Lux T, Marehesi M 1999 Nature 397 498
[31] [32] Yang P, Hou W, Feng G L 2008 Acta Phys. Sin. 57 5333 (in Chinese)[杨 萍、 侯 威、 封国林 2008 物理学报 57 5333]
[33] [34] [35] Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[36] Lee J M, Kin D J, Kim I Y 2002 Computers in Biology and Medicine 32 37
[37] [38] [39] Ott E 1993 Chaos in dynamical systems (Cambridge, UK: Cambridge University Press) p305
[40] Theiler J, Linsay P S 1993 M Rubin Time Series Prediction: Forecasting the Future and Understanding the Past (Addison-Wesley, Reading Mass. Press) p429
[41] [42] [43] Timmer J 1998 Phys. Rev. E 58 5153
[44] [45] Theiler J, Eubank S, Longtin A 1992 Physica D 58 77
[46] Kugiumtzis D 2000 Phys. Rev. E 62 25
[47] [48] [49] Timmer J 2000 Phys. Rev. Lett. 85 2647
[50] [51] Stam C J, Mpijn J P, Pritchard W S 1998 Physica D 112 361
[52] Bernaola G P 2001 Phys. Rev. Lett. 87 168
[53] [54] [55] Oliver J L, Bernaola G P, Carpena P, Romn R R 2001 Gene 276 47
[56] Chernoff H, Lehmann E L 1954 The Annals of Mathematical Statistics 25 579
[57] [58] Plackett R L 1993 International Statistical Review 51 59
[59] [60] [61] Greenwood P E, Nikulin M S 1996 Wiley, New York. ISBN 047155779X
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