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Statistical properties of user activity fluctuations in virtual worlds

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  • Yang, Yan-Hong
  • Xie, Wen-Jie
  • Li, Ming-Xia
  • Jiang, Zhi-Qiang
  • Zhou, Wei-Xing

Abstract

User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1 min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to human’s circadian rhythms and weekly cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity Δα is negatively correlated with the maximum activity (p-value = 0.070) and the time to the maximum activity (p-value = 0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has a stronger impact on the singularity width than large fluctuations.

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  • Yang, Yan-Hong & Xie, Wen-Jie & Li, Ming-Xia & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2017. "Statistical properties of user activity fluctuations in virtual worlds," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 271-278.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:271-278
    DOI: 10.1016/j.chaos.2017.10.036
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    as
    1. A. Grabowski & N. Kruszewska & R. A. Kosiński, 2008. "Properties of on-line social systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(1), pages 107-113, November.
    2. Pont, Oriol & Turiel, Antonio & Pérez-Vicente, Conrad J., 2009. "Empirical evidences of a common multifractal signature in economic, biological and physical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2025-2035.
    3. J.-J. Tseng & S.-P. Li & S.-C. Wang, 2010. "Experimental evidence for the interplay between individual wealth and transaction network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 69-74, January.
    4. Wen-Jie Xie & Zhi-Qiang Jiang & Gao-Feng Gu & Xiong Xiong & Wei-Xing Zhou, 2015. "Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application," Papers 1509.05952, arXiv.org.
    5. Jie-Jun Tseng & Sai-Ping Li & Sun-Chong Wang, 2010. "Experimental evidence for the interplay between individual wealth and transaction network," Papers 1001.3731, arXiv.org.
    6. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089, arXiv.org, revised Oct 2009.
    7. Grabowski, Andrzej, 2007. "Interpersonal interactions and human dynamics in a large social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 363-369.
    8. Thomas Lux, 2004. "Detecting Multifractal Properties In Asset Returns: The Failure Of The "Scaling Estimator"," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 481-491.
    9. Grabowski, Andrzej, 2009. "Opinion formation in a social network: The role of human activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 961-966.
    10. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    11. de Souza, Jeferson & Duarte Queirós, Sílvio M., 2009. "Effective multifractal features of high-frequency price fluctuations time series and ℓ-variability diagrams," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2512-2521.
    12. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    13. Z.-Q. Jiang & L. Guo & W.-X. Zhou, 2007. "Endogenous and exogenous dynamics in the fluctuations of capital fluxes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(3), pages 347-355, June.
    14. Edward Castronova, "undated". "Virtual Worlds: A First-Hand Account of Market and Society on the Cyberian Frontier," Gruter Institute Working Papers on Law, Economics, and Evolutionary Biology 2-1-1008, Berkeley Electronic Press.
    15. Jiang, Zhi-Qiang & Ren, Fei & Gu, Gao-Feng & Tan, Qun-Zhao & Zhou, Wei-Xing, 2010. "Statistical properties of online avatar numbers in a massive multiplayer online role-playing game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 807-814.
    16. Castro e Silva, A. & Moreira, J.G., 1997. "Roughness exponents to calculate multi-affine fractal exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 235(3), pages 327-333.
    17. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    18. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    19. Zhi-Qiang Jiang & Liang Guo & Wei-Xing Zhou, 2007. "Endogenous and exogenous dynamics in the fluctuations of capital fluxes: An empirical analysis of the Chinese stock market," Papers physics/0702035, arXiv.org.
    20. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2007. "Scale invariant distribution and multifractality of volatility multipliers in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 343-350.
    21. Andrzej Grabowski & Natalia Kruszewska, 2007. "Experimental Study Of The Structure Of A Social Network And Human Dynamics In A Virtual Society," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(10), pages 1527-1535.
    22. Edward Castronova, 2001. "Virtual Worlds: A First-Hand Account of Market and Society on the Cyberian Frontier," CESifo Working Paper Series 618, CESifo.
    23. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.
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