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This paper studies the long range correlation of the return intervals of extreme events using the method of percent threshold. In view of return intervals of the extreme events, the long range-correlations of return intervals are studied by simulated time series when the extreme events happened. It is found that the constructed extreme event time series also have the characteristics of long-range correlation if the original time series have one. Meanwhile, the scaling exponents of the two time series are very close, it is very different from the return intervals of stochastic series. The probability density function of time series with long-range correlation has significant difference from the stochastic time series. It was found that there is a group-occurrence phenomenon in the return time series with long-range correlation, so a so-called group occurrence index is defined and computed, the stability of the index is also studied. The results show that the reason of the group occurrence of extreme events series is attributed to the long-range correlation of time series.
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Keywords:
- return interval /
- long-range correlation /
- group-occurrence /
- extreme events
[1] Gumbel E J 1958 Statistics of Extremes(New York: Columbia University Press)
[2] Fisher R A, Tippett L H C 1928 Proc. Camb. Philos.Soc. 24 180
[3] Muzy B, Reg C 1997 Adv. Atmos. Sci. 14 177
[4] Feng G L, Cao H X 1998 Quart. J. Appl. Meteorol. 9 219 (in Chinese) [封国林、曹鸿兴 1998 应用气象学报 9 219]
[5] Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[6] Talkner P, Weber R O 2000 Phys. Rev. E 62 150
[7] Eichner J F, Bunde E K, Bunde A, Havlin S 2003 Phys. Rev. E 68 046133
[8] Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光、支 蓉、张增平 2008 57 5343]
[9] Arneodo A, Bacry E, Graves P V, Muzy J F 1995 Phys. Rev. Lett. 74 16
[10] Bonsal B R, Zhang X B, Vincent L A 2001 J. Clim. 5 1959
[11] Zhang D Q, Feng G L, Hu J G 2008 Chin. Phys. B 17 736
[12] Folland C K, Miller C, Bader D 1999 Clim. Change 42 31
[13] Bunde E K, Bunde A, Havlin S, Goldreich Y 1996 Physica A 231 393
[14] Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E, Goldberger A L 993 Phys. Rev. Lett. 1343 70
[15] Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5494 (in Chinese) [封国林、龚志强、董文杰、李建平 2005 54 5494]
[16] Buldyrev S V, Goldberger A L, Havlin S 1995 Phys. Rev. E 51 5084
[17] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese)[封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[18] Hu K, Ivanov P C, Chen Z, Carpena P 2001 Phys. Rev. E 64 011114
[19] Kantelhardt J W, Bunde E K, Rego H A 2001 Physica A 295 441
[20] Cao H X, Richard B, Yu H Y, He H Z 2006 Trans. Sci. 9 10
[21] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlin. Proc. in Geophys. 15 601
[22] Altmann E G, Kantz H 2005 Phys. Rev. E 71 056106
[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) (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)]
[24] Gilberto E P, Jose A R, Alejandro V 2006 Ann. Nucl. Energy 33 1309
[25] Feng G L, Dong W J 2003 Chin. Phys. 12 1076
[26] Feng G L, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 4 (in Chinese) [封国林、侯 威、龚志强、支 蓉 2009 58 4]
[27] Makse H A, Havlin S, Schwartz M, Stanley H E 1996 Phys. Rev. E 53 5445
[28] Schreiber T, Schmitz A 2000 Physica D 142 346
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[1] Gumbel E J 1958 Statistics of Extremes(New York: Columbia University Press)
[2] Fisher R A, Tippett L H C 1928 Proc. Camb. Philos.Soc. 24 180
[3] Muzy B, Reg C 1997 Adv. Atmos. Sci. 14 177
[4] Feng G L, Cao H X 1998 Quart. J. Appl. Meteorol. 9 219 (in Chinese) [封国林、曹鸿兴 1998 应用气象学报 9 219]
[5] Bunde E K, Bunde A, Havlin S, Roman H E, Goldreich Y, Schellnhuber H J 1998 Phys. Rev. Lett. 81 729
[6] Talkner P, Weber R O 2000 Phys. Rev. E 62 150
[7] Eichner J F, Bunde E K, Bunde A, Havlin S 2003 Phys. Rev. E 68 046133
[8] Wang Q G, Zhi R, Zhang Z P 2008 Acta Phys. Sin. 57 5343 (in Chinese) [王启光、支 蓉、张增平 2008 57 5343]
[9] Arneodo A, Bacry E, Graves P V, Muzy J F 1995 Phys. Rev. Lett. 74 16
[10] Bonsal B R, Zhang X B, Vincent L A 2001 J. Clim. 5 1959
[11] Zhang D Q, Feng G L, Hu J G 2008 Chin. Phys. B 17 736
[12] Folland C K, Miller C, Bader D 1999 Clim. Change 42 31
[13] Bunde E K, Bunde A, Havlin S, Goldreich Y 1996 Physica A 231 393
[14] Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E, Goldberger A L 993 Phys. Rev. Lett. 1343 70
[15] Feng G L, Gong Z Q, Dong W J, Li J P 2005 Acta Phys. Sin. 54 5494 (in Chinese) [封国林、龚志强、董文杰、李建平 2005 54 5494]
[16] Buldyrev S V, Goldberger A L, Havlin S 1995 Phys. Rev. E 51 5084
[17] Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese)[封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[18] Hu K, Ivanov P C, Chen Z, Carpena P 2001 Phys. Rev. E 64 011114
[19] Kantelhardt J W, Bunde E K, Rego H A 2001 Physica A 295 441
[20] Cao H X, Richard B, Yu H Y, He H Z 2006 Trans. Sci. 9 10
[21] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Nonlin. Proc. in Geophys. 15 601
[22] Altmann E G, Kantz H 2005 Phys. Rev. E 71 056106
[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) (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)]
[24] Gilberto E P, Jose A R, Alejandro V 2006 Ann. Nucl. Energy 33 1309
[25] Feng G L, Dong W J 2003 Chin. Phys. 12 1076
[26] Feng G L, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 4 (in Chinese) [封国林、侯 威、龚志强、支 蓉 2009 58 4]
[27] Makse H A, Havlin S, Schwartz M, Stanley H E 1996 Phys. Rev. E 53 5445
[28] Schreiber T, Schmitz A 2000 Physica D 142 346
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