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The detrended fluctuation analysis (DFA) method is used to analyze the human on-line activities in e-commerce. We comprehensively investigate the scale laws of browse and purchase behaviors, which have received little attention before. The time series of browse and purchase behaviors each obviously show a periodical character, and their probability density distributions each have a significant bimodal form. Based on the Fourier transform method, the power spectra of time series indicate that each of them obeys a stochastic process with a long-range self-similar feature (i.e., deviation far from the Poisson process). After identifying and filtering the influence of periodic trend based on power spectra, the detrended fluctuation analysis is used to study the scaling law of time series. Several interesting results can be found that their scaling behaviors on small and large scales show similar values that confirm the long-range correlations rooting in the time series of human on-line activities, and their average scaling exponent approximately equaling 1 suggests that the human online activity may be associated with a self-organized criticality. Although the empirical results are only the observed phenomena like those found in the Internet traffic and stock price fluctuation of financial market, we still think that they may provide an important insight to deeply understand the mechanism of human dynamic behaviors in e-commerce and predict their fluctuation trend for the potential business application.
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Keywords:
- scale law /
- DFA /
- long-range correlation /
- human dynamics
[1] Barabási A L 2005 Nature 435 207
[2] Oliveira J G, Barabási A L 2005 Nature 437 1251
[3] Han X P, Zhou T, Wang B H 2008 New J. Phys. 10 703010
[4] Shang M S, Chen G X, Dai S X, Wang B H, Zhou T 2010 Chin. Phys. Lett. 27 048701
[5] Plerou V, Gopikrishnan P, Amaral L A N, Gabaix X, Stanley H E 2000 Phys. Rev. E 62 R3023
[6] Jiang Z Q, Chen W, Zhou W X 2008 Physica A 387 5818
[7] Dezsö Z, Almaas E, Lukács A, Rácz B, Szakadát I, Barabási A L 2006 Phys. Rev. E 73 066132
[8] Goncalves B, Ramasco J J 2008Phys. Rev. E 78 026123
[9] Zhou T, Kiet H A T, Kim B J, Wang B H, Holme P 2008 Euro. Phys. Lett. 82 28002
[10] Hu H B, Han D Y 2008 Physica A 387 5916
[11] Zhao Z D, Xia H, Shang M S, Zhou T 2011Chin. Phys. Lett. 28 068901
[12] Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛 2012 61 098901]
[13] Henderson T, Bhatti S 2001 Proceedings of the Ninth ACM International Conference on Multimedia Canada, September 30-October 5, 2001 p212
[14] Shang M S, L L Y, Zhang Y C, Zhou T 2010 Euro. Phys. Lett. 90 48006
[15] Takayasu M, Takayasu H, Takamitsu S 1996 Physica A 233 824
[16] Ivanov P C, Amaral L A N, Goldberger A L, Havlin S, Rosenblum M G, Stanley H E, Struzik Z R 2001 Chaos 11 641
[17] AblowitzM J, Kaup D J, Newell A C, Segur H 1974 Stud. Appl. Math. 53 249
[18] Deeming T J 1975 Astrophys. Space Sci. 36 137
[19] Cai S M, Zhou P L, Yang H J, Yang C X, Wang B H, Zhou T 2006 Chin. Phys. Lett. 23 754.
[20] Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441
[21] Chianca C V, Ticona A, Penna T J P 2005 Physica A 357 447
[22] Yang P, Ho W, Feng G L 2008 Acta Phys. Sin. 57 3333 (in Chinese) [杨萍, 候威, 封国林 2008 57 3333]
[23] 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]
[24] Wu J J, Xu S Y, Sun H J 2011 Acta Phys. Sin. 60 019502 (in Chinese) [吴建军, 徐尚义, 孙会君 2011 60 019502]
[25] Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E, Goldberger A L 1993 Phys. Rev. Lett. 70 1343
[26] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[27] Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114
[28] Chen Z, Ivanov P C, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
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[1] Barabási A L 2005 Nature 435 207
[2] Oliveira J G, Barabási A L 2005 Nature 437 1251
[3] Han X P, Zhou T, Wang B H 2008 New J. Phys. 10 703010
[4] Shang M S, Chen G X, Dai S X, Wang B H, Zhou T 2010 Chin. Phys. Lett. 27 048701
[5] Plerou V, Gopikrishnan P, Amaral L A N, Gabaix X, Stanley H E 2000 Phys. Rev. E 62 R3023
[6] Jiang Z Q, Chen W, Zhou W X 2008 Physica A 387 5818
[7] Dezsö Z, Almaas E, Lukács A, Rácz B, Szakadát I, Barabási A L 2006 Phys. Rev. E 73 066132
[8] Goncalves B, Ramasco J J 2008Phys. Rev. E 78 026123
[9] Zhou T, Kiet H A T, Kim B J, Wang B H, Holme P 2008 Euro. Phys. Lett. 82 28002
[10] Hu H B, Han D Y 2008 Physica A 387 5916
[11] Zhao Z D, Xia H, Shang M S, Zhou T 2011Chin. Phys. Lett. 28 068901
[12] Gong K, Tang M, Shang M S, Zhou T 2012 Acta Phys. Sin. 61 098901 (in Chinese) [龚凯, 唐明, 尚明生, 周涛 2012 61 098901]
[13] Henderson T, Bhatti S 2001 Proceedings of the Ninth ACM International Conference on Multimedia Canada, September 30-October 5, 2001 p212
[14] Shang M S, L L Y, Zhang Y C, Zhou T 2010 Euro. Phys. Lett. 90 48006
[15] Takayasu M, Takayasu H, Takamitsu S 1996 Physica A 233 824
[16] Ivanov P C, Amaral L A N, Goldberger A L, Havlin S, Rosenblum M G, Stanley H E, Struzik Z R 2001 Chaos 11 641
[17] AblowitzM J, Kaup D J, Newell A C, Segur H 1974 Stud. Appl. Math. 53 249
[18] Deeming T J 1975 Astrophys. Space Sci. 36 137
[19] Cai S M, Zhou P L, Yang H J, Yang C X, Wang B H, Zhou T 2006 Chin. Phys. Lett. 23 754.
[20] Kantelhardt J W, Koscielny-Bunde E, Rego H H A, Havlin S, Bunde A 2001 Physica A 295 441
[21] Chianca C V, Ticona A, Penna T J P 2005 Physica A 357 447
[22] Yang P, Ho W, Feng G L 2008 Acta Phys. Sin. 57 3333 (in Chinese) [杨萍, 候威, 封国林 2008 57 3333]
[23] 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]
[24] Wu J J, Xu S Y, Sun H J 2011 Acta Phys. Sin. 60 019502 (in Chinese) [吴建军, 徐尚义, 孙会君 2011 60 019502]
[25] Peng C K, Mietus J, Hausdorff J M, Havlin S, Stanley H E, Goldberger A L 1993 Phys. Rev. Lett. 70 1343
[26] Peng C K, Buldyrev S V, Havlin S, Simons M, Stanley H E, Goldberger A L 1994 Phys. Rev. E 49 1685
[27] Hu K, Ivanov P C, Chen Z, Carpena P, Stanley H E 2001 Phys. Rev. E 64 011114
[28] Chen Z, Ivanov P C, Hu K, Stanley H E 2002 Phys. Rev. E 65 041107
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