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This paper presents a functional diagnostic method based on the fractal dimension of time series fluctuations.
The obvious presence of fractal scaling behaviour at all times, and the variation in scaling exponents from quiet to active intervals, suggest that the non-equilibrium magnetosphere system, represented by time series fluctuations, exists in a critical configuration.
The most usual records of observable quantities are in the form of ordered sequences (e.g., time series), fluctuations perpendicular to the surface, and their fractal properties which have been extensively investigated [20].
ReHo measures the local synchronization of the time series of neighboring voxels [ 17] whereas ALFF/fALFF measures the amplitude of time series fluctuations at each voxel [ 18, 19].
Poincare plot analysis provides a visual tool to characterize the complex feature of time series fluctuations and measures the self-similarity in processes [ 25].
Repetitive pattern in time series fluctuations, such as heart rate or metabolism, renders them more predictable whereas small numbers of repetitions in patterns make time series less predictable [ 5].
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These analyses are based on the evaluation of time-series fluctuations across time intervals of increasing size, and were originally introduced in the study of fractals.
Statistical and Fourier analysis methods of time series representing fluctuations of stock market in general and Indian stock markets in particular are well known.
However, the patented version would not work because when many periods are in series, any fluctuation can start domain oscillation as pointed out by Gunn many years ago.
It is shown that there is a series of fluctuation waves and the density oscillations in stellar cores, while the g T effect is responsible for producing the oscillations.
The recently developed technique of wavelet transform based on localized wavelet functions is applicable to the analysis of nonlinear or nonstationary pressure fluctuation signals: the time series of pressure fluctuation signals have been analyzed by means of discrete wavelet transform coefficients and multiresolution decomposition.
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