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Comparison of applications of different filter methods for de-noising detrended fluctuation analysis

Cheng Hai-Ying He Wen-Ping Wu Qiong Zhang Wen

Comparison of applications of different filter methods for de-noising detrended fluctuation analysis

Cheng Hai-Ying, He Wen-Ping, Wu Qiong, Zhang Wen
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  • We studied the effects of continuous noises and random spikes on detrended fluctuation analysis, and found that the noises lead to the appearance of crossovers in the double logarithm curves when the linear fitting scale was less than a characteristic scale s×. To solve this problem, we use three kinds of filter methods, multi-stage Vondrak filter, N-point weighted moving average filter and fast Fourier filter, to filter high frequency from the analyzed time series. The results indicate that the evolution trend and intensity of high frequency series by multi-stage Vondrak filter is almost identical to those of real noises. Further investigation showed that multi-stage Vondrak filter can eliminate the phenomenon of crossover, and the DFA results of lowpass filtering time series are less dependent on the threshold of the filter periods. To some extent, N-points weighted moving average filter can partly eliminate the effect of noises on DFA, but can not completely eliminate the phenomenon of crossover caused by noises. Fast Fourier filter can almost totally eliminate the effect of noises on DFA when the period of filter adopts an appropriate value, but the filtering results have a stronger dependence on the period of filter, so it is difficult to select the period of filter in practical application. Therefore, comparatively speaking, multi-stage Vondrak filter is an effective measure to alleviate the effects of noises on the DFA results.
    • Funds:
    [1]

    He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys.Sin. 55 969 (in Chinese) [何文平、封国林、董文杰、李建平 2006 物理学报 55 969]

    [2]

    Du J 2002 J. Appl. Meteo. Sin. 13 16 (in Chinese) [杜 均 2002 应用气象学报 13 16]

    [3]

    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)]

    [4]

    Zuo H J 2001 Meteorology Journal of Hubei 4 29 (in Chinese) [左惠娟 2001 湖北气象 4 29]

    [5]

    Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 R2239

    [6]

    Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685

    [7]

    Peng C K, Havlin S, Goldberger A L 1995 Chaos 5 82

    [8]

    Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林、王启光、侯 威、龚志强、支 蓉 2009 物理学报 58 2853]

    [9]

    Wang Q G, Hou W, Zheng Z H, Gao R 2009 Acta Phys. Sin. 58 6640 (in Chinese) [王启光、侯 威、郑志海、高 荣 2009 物理学报 58 6640]

    [10]

    Caballero R, Jewson S, Brix A 2002 Clim. Res. 21 127

    [11]

    Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 68 046133-1

    [12]

    Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501

    [13]

    Govindan R B, Vyushin D, Bunde A, Brenner S, Havlin S, Schellnhuber H J 2000 Phys. Rev. Lett. 89 028501

    [14]

    Govindan R B, Vjushin D, Brenner S, Bunder A, Havlin S, Schellnhuber H J 2001 Physica A 294 239

    [15]

    Cao H X, Zheng Z F, Zhang X L, Xie Z, Pan J H 2007 Chin. J. Geophys. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华2007地球物理学报50 420]

    [16]

    He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601

    [17]

    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]

    [18]

    Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107

    [19]

    Vondrak J 1969 Bull. Astron. Inst. Czech. 20 349

    [20]

    Vondrak J 1977 Bull. Astron. Inst. Czech. 28 84

    [21]

    Yan H M, Zhong M, Zhu Y Z 2006 J. Geode. Geody. 26 109 (in Chinese) [闫昊明、钟 敏、朱耀仲 2006大地测量与地球动力学26 109]

    [22]

    Zheng D W, Dong D N 1986 Acta Astro. Sin. 27 368 (in Chinese) [郑大伟、董大南 1986 天文学报 27 368]

    [23]

    Huang K Y, Zhou X 1981 Acta Astro. Sin. 22 121 (in Chinese) [黄坤仪、周 雄 1981 天文学报 22 121]

    [24]

    Wang X L, Ropelewshi C F 1995 J. Climate 8 1584

    [25]

    Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844

    [26]

    Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180

    [27]

    Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311

    [28]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [29]

    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物理学报 50 606]

    [30]

    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 物理学报 51 1181]

    [31]

    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 Obserbational Data (Beijing: Metrological Press) p17 (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17页]

  • [1]

    He W P, Feng G L, Dong W J, Li J P 2006 Acta Phys.Sin. 55 969 (in Chinese) [何文平、封国林、董文杰、李建平 2006 物理学报 55 969]

    [2]

    Du J 2002 J. Appl. Meteo. Sin. 13 16 (in Chinese) [杜 均 2002 应用气象学报 13 16]

    [3]

    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)]

    [4]

    Zuo H J 2001 Meteorology Journal of Hubei 4 29 (in Chinese) [左惠娟 2001 湖北气象 4 29]

    [5]

    Peng C K, Havlin S, Schwartz M, Stanley H E 1991 Phys. Rev. A 44 R2239

    [6]

    Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685

    [7]

    Peng C K, Havlin S, Goldberger A L 1995 Chaos 5 82

    [8]

    Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese) [封国林、王启光、侯 威、龚志强、支 蓉 2009 物理学报 58 2853]

    [9]

    Wang Q G, Hou W, Zheng Z H, Gao R 2009 Acta Phys. Sin. 58 6640 (in Chinese) [王启光、侯 威、郑志海、高 荣 2009 物理学报 58 6640]

    [10]

    Caballero R, Jewson S, Brix A 2002 Clim. Res. 21 127

    [11]

    Eichner J F, Koscienly-Bunde E, Bunde A 2003 Phys. Rev. E 68 046133-1

    [12]

    Fraedrich K, Blender R 2003 Phys. Rev. Lett. 90 108501

    [13]

    Govindan R B, Vyushin D, Bunde A, Brenner S, Havlin S, Schellnhuber H J 2000 Phys. Rev. Lett. 89 028501

    [14]

    Govindan R B, Vjushin D, Brenner S, Bunder A, Havlin S, Schellnhuber H J 2001 Physica A 294 239

    [15]

    Cao H X, Zheng Z F, Zhang X L, Xie Z, Pan J H 2007 Chin. J. Geophys. 50 420 (in Chinese) [曹鸿兴、郑祚芳、张秀丽、谢 庄、潘家华2007地球物理学报50 420]

    [16]

    He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Proc. Geophys. 15 601

    [17]

    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]

    [18]

    Chen Z, Ivanov P, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107

    [19]

    Vondrak J 1969 Bull. Astron. Inst. Czech. 20 349

    [20]

    Vondrak J 1977 Bull. Astron. Inst. Czech. 28 84

    [21]

    Yan H M, Zhong M, Zhu Y Z 2006 J. Geode. Geody. 26 109 (in Chinese) [闫昊明、钟 敏、朱耀仲 2006大地测量与地球动力学26 109]

    [22]

    Zheng D W, Dong D N 1986 Acta Astro. Sin. 27 368 (in Chinese) [郑大伟、董大南 1986 天文学报 27 368]

    [23]

    Huang K Y, Zhou X 1981 Acta Astro. Sin. 22 121 (in Chinese) [黄坤仪、周 雄 1981 天文学报 22 121]

    [24]

    Wang X L, Ropelewshi C F 1995 J. Climate 8 1584

    [25]

    Shi N, Gu J Q, Yi Y M, Lin Z N 2005 Chin. Phys. 14 844

    [26]

    Shi N, Yi Y M, Gu J Q, Xia D D 2006 Chin. Phys. 15 2180

    [27]

    Zhang W, Wan S Q 2008 Chin. Phys. B 17 2311

    [28]

    Lorenz E N 1963 J. Atmos. Sci. 20 130

    [29]

    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物理学报 50 606]

    [30]

    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 物理学报 51 1181]

    [31]

    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 Obserbational Data (Beijing: Metrological Press) p17 (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17页]

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  • Received Date:  04 May 2010
  • Accepted Date:  13 May 2010
  • Published Online:  05 January 2011

Comparison of applications of different filter methods for de-noising detrended fluctuation analysis

  • 1. (1)Fundamental Education Department, Yancheng Institute of Technology, Yancheng 224002, China; (2)National Climate Center, China Meteorological Administration, Beijing 100081, China; (3)National Satellite Meteorological Center, China Meteorological Administration, Beijing 100081, China; (4)Tongda College, Nanjing University of Post and Telecommunications, Nanjing 210003, China

Abstract: We studied the effects of continuous noises and random spikes on detrended fluctuation analysis, and found that the noises lead to the appearance of crossovers in the double logarithm curves when the linear fitting scale was less than a characteristic scale s×. To solve this problem, we use three kinds of filter methods, multi-stage Vondrak filter, N-point weighted moving average filter and fast Fourier filter, to filter high frequency from the analyzed time series. The results indicate that the evolution trend and intensity of high frequency series by multi-stage Vondrak filter is almost identical to those of real noises. Further investigation showed that multi-stage Vondrak filter can eliminate the phenomenon of crossover, and the DFA results of lowpass filtering time series are less dependent on the threshold of the filter periods. To some extent, N-points weighted moving average filter can partly eliminate the effect of noises on DFA, but can not completely eliminate the phenomenon of crossover caused by noises. Fast Fourier filter can almost totally eliminate the effect of noises on DFA when the period of filter adopts an appropriate value, but the filtering results have a stronger dependence on the period of filter, so it is difficult to select the period of filter in practical application. Therefore, comparatively speaking, multi-stage Vondrak filter is an effective measure to alleviate the effects of noises on the DFA results.

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