The information is held in those properties of the time series that are invariant-i.e. not supposed to change over either time or space. |
Allan scaling exponent |
The time series is modeled as a point process, and the ratio between the second order moment of the difference between the number of events of two successive windows and the mean number of events has scale-invariant properties |
Point process |
[49,89,90] |
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Detrended fluctuation analysis |
The standard deviation of the detrended cumulative time series has scale-invariant properties |
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[4,63,92-94] |
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Diffusion Entropy |
The time series is modeled as a family of diffusion processes, which Shannon entropies has scale-invariant properties |
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[54,95-97] |
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Embedding scaling exponent |
The variance of the attractor at different embedding dimensions has scale-invariant properties |
Phase space representation |
[98] |
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Fano scaling exponent |
The time series is modeled as a point process, and the variance of the number of events divided by the mean number of events has scale-invariant properties |
Point process |
[49,89,90] |
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Higuchi's algorithm |
The length of the time series at different windows has scale-invariant properties |
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[54,101-104] |
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Index of variability |
The time series is modeled as a point process, and the variance of the number of events has scale-invariant properties |
Point process |
[2] |
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Multifractal exponents |
Multiple scaling exponents characterize the time series |
Wavelet transform |
[54,105,106] |
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Power spectrum scaling exponent |
Stationarity, the power spectrum follows a 1/fb like behaviour |
Power spectrum |
[92] |
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Probability distribution scaling exponent |
The distribution of the data has scale--invariant properties |
Bin transformation |
[63,107] |
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Rescaled detrended range analysis |
The range (difference between maximum and minimum value) of a time series has scale-invariant properties |
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[92] |
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Scaled windowed variance |
The standard deviation of the detrended time series has scale-invariant properties |
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[92] |
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Correlation dimension |
The time series is extracted from a dynamical system, and the number of points in the phase space that are closer than a certain threshold has scale-invariant properties |
Phase space representation |
[40,91] |
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Finite growth rates |
The time series is extracted from a dynamical system, which is described by its dependence on the initial conditions (how two points that are close in space and time separate after a certain amount of time)-the ratio between the final and the initial time is an invariant of the system |
Phase space representation |
[86] |
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Kolmogorov-Sinai entropy |
The time series is extracted from a dynamical system, and it is possible to predict which part of the phase space the dynamics will visit at a time t+1, given the trajectories up to time t |
Phase space representation |
[40,91] |
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Largest Lyapunov exponent |
The time series is extracted from a dynamical system, which is described by its dependence on the initial conditions (how two points that are close in space and time separate after a certain amount of time)-the distance grows on average exponentially in time, and the exponent is an invariant of the system |
Phase space representation |
[40,41,99,100] |