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Fractal dimensions of time sequences

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  • Liaw, Sy-Sang
  • Chiu, Feng-Yuan

Abstract

We present a simple and efficient way for calculating the fractal dimension D of any time sequence sampled at a constant time interval. We calculated the error of a piecewise interpolation to N+1 points of the time sequence with respect to the next level of (2N+1)-point interpolation. This error was found to be proportional to the scale (i.e., 1/N) to the power of 1−D. A simple analysis showed that our method is equivalent to the inverse process of the method of random midpoint displacement widely used in generating fractal Brownian motion for a given D. The efficiency of our method makes the fractal dimension a practical tool in analyzing the abundant data in natural, economic, and social sciences.

Suggested Citation

  • Liaw, Sy-Sang & Chiu, Feng-Yuan, 2009. "Fractal dimensions of time sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3100-3106.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:15:p:3100-3106
    DOI: 10.1016/j.physa.2009.04.011
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    Cited by:

    1. Chang, Tian-Pau & Ko, Hong-Hsi & Liu, Feng-Jiao & Chen, Pai-Hsun & Chang, Ying-Pin & Liang, Ying-Hsin & Jang, Horng-Yuan & Lin, Tsung-Chi & Chen, Yi-Hwa, 2012. "Fractal dimension of wind speed time series," Applied Energy, Elsevier, vol. 93(C), pages 742-749.
    2. Sy-Sang Liaw & Jiann-Yeu Chen, 2017. "Characterizing Sleep Stages by the Fractal Dimensions of Electroencephalograms," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 2(2), pages 41-47, July.
    3. Truong Ngoc Cuong & Le Ngoc Bao Long & Hwan-Seong Kim & Sam-Sang You, 2023. "Data analytics and throughput forecasting in port management systems against disruptions: a case study of Busan Port," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 25(1), pages 61-89, March.

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