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Zbl 0649.58046
Higuchi, T.
Approach to an irregular time series on the basis of the fractal theory. (English)
[J] Physica D 31, No.2, 277-283 (1988). ISSN 0167-2789

We present a technique to measure the fractal dimension of the set of points (t,f(t)) forming the graph of a function f defined on the unit interval. First we apply it to a fractional Brownian function which has a property of self-similarity for all scales, and we can get the stable and precise fractal dimension. This technique is also applied to the observational data of natural phenomena. It does not show self-similarity all over the scale but has a different self-similarity across the characteristic time scale. The present method gives us a stable characteristic time scale as well as the fractal dimension.

MSC 2000:: *58Z05 Appl. of global analysis to physics
37D45 Strange attractors, chaotic dynamics
62M10 Time series, etc. (statistics)

Keywords: fractal dimension; fractional Brownian function

Cited in: Zbl 1166.62068 Zbl 1129.92049 Zbl 1154.92319 Zbl 1031.92018 Zbl 0903.58033

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