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Approach to an irregular time series on the basis of the fractal theory. (English) Zbl 0649.58046
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.

58Z05Applicatons of global analysis to physics
37D45Strange attractors, chaotic dynamics
62M10Time series, auto-correlation, regression, etc. (statistics)
Full Text: DOI
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