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The scaling exponent is an effective nonlinear dynamic index, which can be used to detect the dynamic structure mutations of the correlation time series by the moving cut a fixed window technology. The immediacy and accuracy of scaling exponent is very important for detecting the series change points, however, some of the existing scale index calculation methods (such as rescaled range analysis and rescaled variance analysis) take none of these into account. Wavelet transform analysis can quickly decompose the sequence on different scales, and then the scaling index can be calculated by analyzing the scaling relation of wavelet coefficients on different scales, which has the characteristics of fast calculation speed and good convergence and memory saving. By moving cut window technology, in the present paper we put forward a new method, i. e., the moving cut data-wavelet transformation for detecting a series of dynamic structure mutations. The principle is that the removal of the data has little effect on the estimation of the scaling exponents of the correlation time series with the same dynamical properties. In order to test the performance of the method, first of all, the dynamic structure mutation analyses of linear ideal time series and nonlinear ideal time series are carried out by selecting different moving cut fixed windows. The test results show that the method can quickly and accurately detect the dynamic structure change points and intervals both in linear time series and nonlinear time series, besides, its calculation speed is obviously better than the moving cut data-rescaled range analysis and the moving cut data-rescaled variance analysis. It has strong stability, and depends less on the moving cut window length, which will have some advantages in the large data processing. At the same time, in order to detect the influence of noise on the method, the linear and nonlinear ideal time series are added to the white Gaussian noise (SNR=20, 25, 30 dB), respectively, and the results show that the method has a strong anti-noise ability with different moving cut window lengths, can still quickly and accurately detect the mutation point or interval in different noise additions. Finally, the method is used to detect the dynamic structure mutation of measured daily maximum temperature data of Foping station in Wei basin, the experimental results indicate that the mutation interval is consistent with the abrupt change in 1970's on a global scale, which further verifies the validity of the method.
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Keywords:
- scaling exponent /
- wavelet analysis /
- moving cut data-wavelet transformation analysis /
- mutations detection
[1] Rehman S, Siddiqi A H 2009 Chaos Soliton. Fract. 40 1081
[2] He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[3] 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物理学报58 2862]
[4] He W P, Deng B S, Wu Q, Zhang W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese)[何文平, 邓北胜, 吴琼, 张文, 成海英2010物理学报59 8264]
[5] Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese)[孙东永, 张洪波, 黄强 2014 物理学报 63 209203]
[6] Hurst H E 1951 Trans. Am. Soc. Civ. Eng. 116 770
[7] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[8] Simonsen I, Hansen A, Nes O M 1998 Phys. Rev. E 58 2779
[9] Veitch D, Abry P C 1999 IEEE Trans. Inf. Theory 45 878
[10] Jones C L, Lonergan G T, Mainwaring D E 1996 J. Phys. A:Math. Gen. 29 2509
[11] Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114
[12] Gloter A, Hoffmann M 2007 Ann. Stat. 35 1947
[13] Manimaran P, Panigrahi P K, Parikh J C 2005 Phys. Rev. E 72 046120
[14] Ciftlikli C, Gezer A 2010 Turk. J. Elec. Eng. Comp. Sci. 18 117
[15] Wu L, Ding Y M 2015 Int. J. Wavelets Multiresolut Inf. Process. 13 1550044
[16] Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econom. 112 265
[17] Clausel M, Roueff F, Taqqu M S, Tudor C 2014 Esaim Probab. Stat. 18 42
[18] Taqqu M S, Teverovsky V 1997 Comm. Stat. Stoch. Model 13 723
[19] Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172
[20] Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441
[21] Matos J A O, Gama S M A, Ruskin H J, Sharkasi A A, Crane M 2008 Physica A 387 3910
[22] Mielniczuk J, Wojdyllo P 2007 Comput. Stat. Data Anal. 51 4510
[23] Zhao Y Z, Wu L W 2014 Comput. Eng. Appl. 50 154 (in Chinese)[赵彦仲, 吴立文2014计算机工程与应用50 154]
[24] Dang T D, Molnar S 1999 Period. Polytech, Electr. Eng. 43 227
[25] Giordano S, Miduri S, Pagano M, Russo F, Tartarelli S 1997 Proceedings of 13th International Conference on Digital Signal Processing Santorini, Greece, July 2-4, 1997 p479
[26] Li X B, Ding J, Li H Q 1999 Adv. Water Sci. 10 144 (in Chinese)[李贤彬, 丁晶, 李后强 1999 水科学进展 10 144]
[27] Li X B, Ding J, Li H Q 1998 J. Hydraul. Eng. 8 21 (in Chinese)[李贤彬, 丁晶, 李后强 1998 水利学报 8 21]
[28] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)[王启光, 张增平 2008 物理学报 57 1976]
[29] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese)[何文平, 何涛, 成海英, 张文, 吴琼2011物理学报60 049202]
[30] Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese)[金红梅, 何文平, 张文, 冯爱霞, 侯威2012物理学报61 129202]
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[32] Powell A M, Xu J J 2011 Theor. Appl. Climatol. 104 443
[33] Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese)[封国林, 龚志强, 支蓉2008气象学报66 892]
[34] Shi N, Chen J Q, Tu Q P 1995 Acta Meteor. Sin. 53 431 (in Chinese)[施能, 陈家其, 屠其璞1995气象学报53 431]
[35] Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201
[36] Wu H, Hou W, Yan P C, Zhang Z S, Wang K 2015 Chin. Phys. B 24 089201
[37] Zhang M L, Qu H, Xie X R, Kurths J 2017 Neurocomputing 219 333
[38] Wan L, Zhang Y, Lin J, Jiang C D, Lin T T 2016 Chin. J. Geophys. 59 2290 (in Chinese)[万玲, 张扬, 林君, 蒋川东, 林婷婷2016地球物理学报59 2290]
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[1] Rehman S, Siddiqi A H 2009 Chaos Soliton. Fract. 40 1081
[2] He W P, Feng G L, Wu Q, He T, Wan S Q, Chou J F 2012 Int. J. Climatol. 32 1604
[3] 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物理学报58 2862]
[4] He W P, Deng B S, Wu Q, Zhang W, Cheng H Y 2010 Acta Phys. Sin. 59 8264 (in Chinese)[何文平, 邓北胜, 吴琼, 张文, 成海英2010物理学报59 8264]
[5] Sun D Y, Zhang H B, Huang Q 2014 Acta Phys. Sin. 63 209203 (in Chinese)[孙东永, 张洪波, 黄强 2014 物理学报 63 209203]
[6] Hurst H E 1951 Trans. Am. Soc. Civ. Eng. 116 770
[7] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[8] Simonsen I, Hansen A, Nes O M 1998 Phys. Rev. E 58 2779
[9] Veitch D, Abry P C 1999 IEEE Trans. Inf. Theory 45 878
[10] Jones C L, Lonergan G T, Mainwaring D E 1996 J. Phys. A:Math. Gen. 29 2509
[11] Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114
[12] Gloter A, Hoffmann M 2007 Ann. Stat. 35 1947
[13] Manimaran P, Panigrahi P K, Parikh J C 2005 Phys. Rev. E 72 046120
[14] Ciftlikli C, Gezer A 2010 Turk. J. Elec. Eng. Comp. Sci. 18 117
[15] Wu L, Ding Y M 2015 Int. J. Wavelets Multiresolut Inf. Process. 13 1550044
[16] Giraitis L, Kokoszka P, Leipus R, Teyssiere G 2003 J. Econom. 112 265
[17] Clausel M, Roueff F, Taqqu M S, Tudor C 2014 Esaim Probab. Stat. 18 42
[18] Taqqu M S, Teverovsky V 1997 Comm. Stat. Stoch. Model 13 723
[19] Cajueiro D O, Tabak B M 2005 Math. Comp. Sim. 70 172
[20] Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441
[21] Matos J A O, Gama S M A, Ruskin H J, Sharkasi A A, Crane M 2008 Physica A 387 3910
[22] Mielniczuk J, Wojdyllo P 2007 Comput. Stat. Data Anal. 51 4510
[23] Zhao Y Z, Wu L W 2014 Comput. Eng. Appl. 50 154 (in Chinese)[赵彦仲, 吴立文2014计算机工程与应用50 154]
[24] Dang T D, Molnar S 1999 Period. Polytech, Electr. Eng. 43 227
[25] Giordano S, Miduri S, Pagano M, Russo F, Tartarelli S 1997 Proceedings of 13th International Conference on Digital Signal Processing Santorini, Greece, July 2-4, 1997 p479
[26] Li X B, Ding J, Li H Q 1999 Adv. Water Sci. 10 144 (in Chinese)[李贤彬, 丁晶, 李后强 1999 水科学进展 10 144]
[27] Li X B, Ding J, Li H Q 1998 J. Hydraul. Eng. 8 21 (in Chinese)[李贤彬, 丁晶, 李后强 1998 水利学报 8 21]
[28] Wang Q G, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese)[王启光, 张增平 2008 物理学报 57 1976]
[29] He W P, He T, Cheng H Y, Zhang W, Wu Q 2011 Acta Phys. Sin. 60 049202 (in Chinese)[何文平, 何涛, 成海英, 张文, 吴琼2011物理学报60 049202]
[30] Jin H M, He W P, Zhang W, Feng A X, Hou W 2012 Acta Phys. Sin. 61 129202 (in Chinese)[金红梅, 何文平, 张文, 冯爱霞, 侯威2012物理学报61 129202]
[31] He W P, Liu Q Q, Jiang Y D, Lu Y 2015 Chin. Phys. B 24 049205
[32] Powell A M, Xu J J 2011 Theor. Appl. Climatol. 104 443
[33] Feng G L, Gong Z Q, Zhi R 2008 Acta Meteor. Sin. 66 892 (in Chinese)[封国林, 龚志强, 支蓉2008气象学报66 892]
[34] Shi N, Chen J Q, Tu Q P 1995 Acta Meteor. Sin. 53 431 (in Chinese)[施能, 陈家其, 屠其璞1995气象学报53 431]
[35] Tong J L, Wu H, Hou W, He W P, Zhou J 2014 Chin. Phys. B 23 049201
[36] Wu H, Hou W, Yan P C, Zhang Z S, Wang K 2015 Chin. Phys. B 24 089201
[37] Zhang M L, Qu H, Xie X R, Kurths J 2017 Neurocomputing 219 333
[38] Wan L, Zhang Y, Lin J, Jiang C D, Lin T T 2016 Chin. J. Geophys. 59 2290 (in Chinese)[万玲, 张扬, 林君, 蒋川东, 林婷婷2016地球物理学报59 2290]
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