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For a stable dynamic system, probability density distribution (PDD) of a system variable is relatively stable, and if there is a change in dynamic structure of a system, the PDD of the system variable will have some change correspondingly. According to this characteristic of PDD of a dynamic system, in this paper we present two new methods, namely, skewness index and kurtosis index, to detect an abrupt change in a time series by means of identifying some small changes in PDD. Tests on model time series indicate that skewness index and kurtosis index can be used to identify an abrupt change, such as abrupt change in parameter of an equation and abrupt dynamic change. Thus, we provide a new approach to detecting abrupt change in time series based on PDD. Further studies show that the detected results of the skewness index and kurtosis index are almost independence of the length of a subseries.
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Keywords:
- coefficient of skewness /
- coefficient of kurtosis /
- probability density distribution /
- abrupt change detection
[1] Ye D Z, Tao S Y, Li M C 1958 Acta Metro. Sin. 29 249 (in Chinese) [叶笃正, 陶诗言, 李麦春 1958 气象学报 29 249]
[2] Krishinamulti T N, Ramanathan Y 1982 J. Atmos. Sci. 39 1290
[3] Marten S, Jordi B, William A B, Victor B, Stephen R C, Vasilis D, Hermann H, Egbert H V N, Max R, George S 2009 Nature 461 53
[4] Li Y C, Yan W, Jiang C S, Zuo Y L 2009 Recent Developments inWorld Seismology 369 1 (in Chinese) [李迎春, 闫伟, 蒋长胜, 左玲玉 2009 国际地震动态 369 1]
[5] He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University)(in Chinese) [何文平 2008 博士学位论文 (兰州:兰州大学)]
[6] Mann H B 1945 Econometrica 13 245
[7] Kendall M G, Charles G 1975 Rank Correlation Methods (NewYork: Oxford University) p202
[8] Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan.63 1157
[9] Livina V N, Havlin S, Bunde A 2005 Phys. Rev. Lett. 95 208501
[10] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc.Geophys. 15 601
[11] He W P, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 598264 (in Chinese) [何文平, 吴琼, 张文, 成海英 2010 物理学报 59 8264]
[12] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[13] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[14] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006Nonlinear Theories and Methods on Spatial-Temporal Distribu-tion of the Obserbational Data (Beijing: Metrological Press)pp27–89 (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27——第89页]
[15] He W P, Wu Q, Zheng 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 物理学报 58 2862]
[16] Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[17] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 物理学报 57 1996]
[18] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin.60 813 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 物理学报 60 813]
[19] Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. SignalProcessing 15 2295
[20] Abhisek U, Rastko Z 2006 Electric Power Systems Research 76815
[21] May R 1976 Nature 261 459
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[1] Ye D Z, Tao S Y, Li M C 1958 Acta Metro. Sin. 29 249 (in Chinese) [叶笃正, 陶诗言, 李麦春 1958 气象学报 29 249]
[2] Krishinamulti T N, Ramanathan Y 1982 J. Atmos. Sci. 39 1290
[3] Marten S, Jordi B, William A B, Victor B, Stephen R C, Vasilis D, Hermann H, Egbert H V N, Max R, George S 2009 Nature 461 53
[4] Li Y C, Yan W, Jiang C S, Zuo Y L 2009 Recent Developments inWorld Seismology 369 1 (in Chinese) [李迎春, 闫伟, 蒋长胜, 左玲玉 2009 国际地震动态 369 1]
[5] He W P 2008 Ph. D. Dissertation (Lanzhou: Lanzhou University)(in Chinese) [何文平 2008 博士学位论文 (兰州:兰州大学)]
[6] Mann H B 1945 Econometrica 13 245
[7] Kendall M G, Charles G 1975 Rank Correlation Methods (NewYork: Oxford University) p202
[8] Yamamoto R, Iwashima T, Sanga N K 1985 J. Meteor. Soc. Japan.63 1157
[9] Livina V N, Havlin S, Bunde A 2005 Phys. Rev. Lett. 95 208501
[10] He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc.Geophys. 15 601
[11] He W P, Wu Q, Zheng W, Cheng H Y 2010 Acta Phys. Sin. 598264 (in Chinese) [何文平, 吴琼, 张文, 成海英 2010 物理学报 59 8264]
[12] Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844
[13] Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180
[14] Feng G L, Dong W J, Gong Z Q, Hou W, Wan S Q, Zhi R 2006Nonlinear Theories and Methods on Spatial-Temporal Distribu-tion of the Obserbational Data (Beijing: Metrological Press)pp27–89 (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27——第89页]
[15] He W P, Wu Q, Zheng 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 物理学报 58 2862]
[16] Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311
[17] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1996 (in Chinese) [王启光, 张增平 2008 物理学报 57 1996]
[18] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin.60 813 (in Chinese) [何文平, 何涛, 成海英, 张文, 吴琼 2011 物理学报 60 813]
[19] Babak A S, Krishnaprasad P S 2004 EURASIP J. Appl. SignalProcessing 15 2295
[20] Abhisek U, Rastko Z 2006 Electric Power Systems Research 76815
[21] May R 1976 Nature 261 459
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