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 ( 2 N + 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.
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