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Simple correlation dimension estimator and its use to detect causality

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  • Krakovská, Anna
  • Chvosteková, Martina

Abstract

Revisiting the Grassberger–Procaccia algorithm inspires us to introduce an extremely simple estimator of the correlation dimension. For the new estimator, we also provide guidance on determining the extent to which the correlation dimension may be underestimated, given the size of the data and the dimensionality of the state space.

Suggested Citation

  • Krakovská, Anna & Chvosteková, Martina, 2023. "Simple correlation dimension estimator and its use to detect causality," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008767
    DOI: 10.1016/j.chaos.2023.113975
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    References listed on IDEAS

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    1. P. Campadelli & E. Casiraghi & C. Ceruti & A. Rozza, 2015. "Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-21, October.
    2. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    3. Pierre Frankhauser, 1998. "Fractal geometry of urban patterns and their morphogenesis," Discrete Dynamics in Nature and Society, Hindawi, vol. 2, pages 1-19, January.
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