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Two general models that generate long range correlation

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  • Gan, Xiaocong
  • Han, Zhangang

Abstract

In this paper we study two models that generate sequences with LRC (long range correlation). For the IFT (inverse Fourier transform) model, our conclusion is the low frequency part leads to LRC, while the high frequency part tends to eliminate it. Therefore, a typical method to generate a sequence with LRC is multiplying the spectrum of a white noise sequence by a decaying function. A special case is analyzed: the linear combination of a smooth curve and a white noise sequence, in which the DFA plot consists of two line segments. For the patch model, our conclusion is long subsequences leads to LRC, while short subsequences tend to eliminate it. Therefore, we can generate a sequence with LRC by using a fat-tailed PDF (probability distribution function) of the length of the subsequences. A special case is also analyzed: if a patch model with long subsequences is mixed with a white noise sequence, the DFA plot will consist of two line segments. We have checked known models and actual data, and found they are all consistent with this study.

Suggested Citation

  • Gan, Xiaocong & Han, Zhangang, 2012. "Two general models that generate long range correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3477-3483.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:12:p:3477-3483
    DOI: 10.1016/j.physa.2012.02.015
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    References listed on IDEAS

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    1. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    2. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
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    1. Papapetrou, M. & Kugiumtzis, D., 2020. "Tsallis conditional mutual information in investigating long range correlation in symbol sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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