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We develop a method to compute the segment size in the detrended fluctuation analysis (DFA), which is based on the basic concept of the information theory, and verify the method effectiveness by numerical experiment. This method is freed from the problem of subjectivity in the former process to choose the segment size which usually leads to false result. We Change the length of sequence with dynamics being the same, the results remain stable. The results indicate that when the length of sequence is too short, even the optimal selection of segment size is not enough for the portrait of the overall dynamic system, thus the DFA cannot be used in this circumstance. The method we developed in this paper can enhance the reliability of DFA results by judging whether the sequences analyzed meet the requirements of DFA. We also obtain the DFA index from 1961 to 2000 of China through DFA method and analyze its spatial characteristics of distribution.
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Keywords:
- detrended fluctuation analysis /
- parameter selection /
- segment /
- optimal selection
[1] Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[2] Lux T, Marehesi M 1999 Nature 397 498
[3] Mantegna R N, Stanley H E 1995 Nature 376 46
[4] Liu F, Shan X M, Ren Y, Zhang J, Ma Z X 2004 Acta Phys. Sin. 53 550 (in Chinese)[刘 锋、 山秀明、 任 勇、 张 军、 马正新 2004 53 550]
[5] Sealas E 1998 Physica A 253 394
[6] Janosi I M, Janeesko B, Kondor D 1999 Physica A 269 111
[7] 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 58 2853] 〖8] Stanley H E, Amaral L A N, Canning D 1999 Physica A 269 156
[8] Stanley H E, Afanasyevr V, Anlaral L A N 1996 Physica A 224 302
[9] 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]
[10] 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 58 2862] 〖12] Govindan R B, Vjushin D, Brenner S 2001 Physica A 294 239
[11] Kantelhardta J W, Zschiegner S A, Bunde E K 2002 Physica A 316 87
[12] Bernaola G P 2001 Phys. Rev. Lett. 87 168
[13] 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 58 6640]
[14] Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[15] Lee J M, Kin D J, Kim I Y 2002 Comp. Bio. Med. 32 37
[16] Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press) pp305—333
[17] Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[18] Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 56 3152]
[19] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红、 阎桂荣、 韩宇航 2005 54 550]
[20] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[21] Yang Z A, Wang G R, Chen S G 1995 Chin. J. Comp. Phys. 12 442 (in Chinese)[杨志安、 王光瑞、 陈式刚 1995 计算物理 12 442]
[22] Nichols J M, Nichols J D 2001 Math. Biosci. 171 21
[23] Rechester A B, White R B 1991 Phys. Lett. A 156 419
[24] Rechester A B, White R B 1997 Phys. Rev. Lett. 78 54
[25] Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164
[26] Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
[27] Azad R K, Rao J S, Ramaswamy R 2002 Chaos Solitions Fract. 14 633
[28] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese)[肖方红、 阎桂荣、 韩宇航 2004 53 2877]
[29] Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese)[郑志海、 任宏利、 黄建平 2009 58 7359]
[30] Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164501
[31] Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
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[1] Peng C K, Buldyrev S V, Havlin S 1994 Phys. Rev. E 49 1685
[2] Lux T, Marehesi M 1999 Nature 397 498
[3] Mantegna R N, Stanley H E 1995 Nature 376 46
[4] Liu F, Shan X M, Ren Y, Zhang J, Ma Z X 2004 Acta Phys. Sin. 53 550 (in Chinese)[刘 锋、 山秀明、 任 勇、 张 军、 马正新 2004 53 550]
[5] Sealas E 1998 Physica A 253 394
[6] Janosi I M, Janeesko B, Kondor D 1999 Physica A 269 111
[7] 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 58 2853] 〖8] Stanley H E, Amaral L A N, Canning D 1999 Physica A 269 156
[8] Stanley H E, Afanasyevr V, Anlaral L A N 1996 Physica A 224 302
[9] 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]
[10] 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 58 2862] 〖12] Govindan R B, Vjushin D, Brenner S 2001 Physica A 294 239
[11] Kantelhardta J W, Zschiegner S A, Bunde E K 2002 Physica A 316 87
[12] Bernaola G P 2001 Phys. Rev. Lett. 87 168
[13] 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 58 6640]
[14] Panlov A N, Sosnovtseva O V, Ziganshin A R 2002 Physica A 316 233
[15] Lee J M, Kin D J, Kim I Y 2002 Comp. Bio. Med. 32 37
[16] Ott E 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press) pp305—333
[17] Yang X L, Xu W 2008 Chin. Phys. B 17 2004
[18] Zhang D Z 2007 Acta Phys. Sin. 56 3152 (in Chinese) [张佃中 2007 56 3152]
[19] Xiao F H, Yan G R, Han Y H 2005 Acta Phys. Sin. 54 550 (in Chinese) [肖方红、 阎桂荣、 韩宇航 2005 54 550]
[20] Fraser A M, Swinney H L 1986 Phys. Rev. A 33 1134
[21] Yang Z A, Wang G R, Chen S G 1995 Chin. J. Comp. Phys. 12 442 (in Chinese)[杨志安、 王光瑞、 陈式刚 1995 计算物理 12 442]
[22] Nichols J M, Nichols J D 2001 Math. Biosci. 171 21
[23] Rechester A B, White R B 1991 Phys. Lett. A 156 419
[24] Rechester A B, White R B 1997 Phys. Rev. Lett. 78 54
[25] Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164
[26] Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
[27] Azad R K, Rao J S, Ramaswamy R 2002 Chaos Solitions Fract. 14 633
[28] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 2877 (in Chinese)[肖方红、 阎桂荣、 韩宇航 2004 53 2877]
[29] Zheng Z H, Ren H L, Huang J P 2009 Acta Phys. Sin. 58 7359 (in Chinese)[郑志海、 任宏利、 黄建平 2009 58 7359]
[30] Lehrman M, Rechester A B 2001 Phys. Rev. Lett. 87 164501
[31] Liu Z H, Chen S G 1997 Phys. Rev. E 56 7297
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