Fractal dimensions of time sequences

Sy-Sang Liaw and Feng-Yuan Chiu

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 15, 3100-3106

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.

Keywords: Fractal dimension; Time sequence; Stock index; Fractal Brownian motion; Random walk (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:15:p:3100-3106

DOI: 10.1016/j.physa.2009.04.011

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