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Enhanced box and prism assisted algorithms for computing the correlation dimension

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  • Bueno-Orovio, Alfonso
  • Pérez-García, Víctor M.

Abstract

Box-assisted and prism-assisted algorithms are among the most popular algorithms for the computation of the correlation dimension. However, the box size is usually determined by authors just through rough estimates or even by trial and error. In this paper, an explicit criterion for the selection of the optimal box size in box-assisted algorithms is presented. When used in conjunction with even the simplest box-assisted algorithm, the computation time needed to estimate the correlation integral is drastically reduced. These reductions range from a factor of 10 to factors larger than 1000, depending on the complexity of the attractor and/or the length of the dataset.

Suggested Citation

  • Bueno-Orovio, Alfonso & Pérez-García, Víctor M., 2007. "Enhanced box and prism assisted algorithms for computing the correlation dimension," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 509-518.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:509-518
    DOI: 10.1016/j.chaos.2006.03.043
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    1. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    2. Pascolo, Paolo & Barazza, Fausto & Carniel, Roberto, 2006. "Considerations on the application of the chaos paradigm to describe the postural sway," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1339-1346.
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    1. Zhou, Shuang & Wang, Xingyuan & Zhou, Wenjie & Zhang, Chuan, 2022. "Recognition of the scale-free interval for calculating the correlation dimension using machine learning from chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).

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