fractal-analysis 0.1.2

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Fractal Analysis

Fractal and multifractal methods, including

• fractional Brownian motion (FBM) tester
• multifractional Brownian motion (MBM) tester

To install

To get started, simply do:

pip install fractal-analysis

or check out the code from out GitHub repository.

You can now use the package in Python with:

from fractal_analysis import tester

Examples

Import:

from fractal_analysis.tester.series_tester import MBMSeriesTester, FBMSeriesTester
from fractal_analysis.tester.critical_surface import CriticalSurfaceFBM, CriticalSurfaceMFBM

To test if a series series is FBM, one needs to use CriticalSurfaceFBM with length of the series N and the significance level alpha (look at quantiles of order alpha/2 and 1 − alpha/2)

fbm_tester = FBMSeriesTester(critical_surface=CriticalSurfaceFBM(N=N, alpha=0.05))

To test if the series is FBM with holder exponent 0.3 and use auto estimated sigma square (set sig2=None):

is_fbm, sig2 = fbm_tester.test(h=0.3, x=series, sig2=None)

If the output contains, for example:

Bad auto sigma square calculated with error 6.239236333681868. Suggest to give sigma square and rerun.

The auto sigma square estimated is not accurate. One may want to manually choose a sigma square and rerun. For example:

is_fbm, sig2 = fbm_tester.test(h=0.3, x=series, sig2=1)

To test if the series is MBM, one needs to use CriticalSurfaceMFBM with length of the series N and the significance level alpha (look at quantiles of order alpha/2 and 1 − alpha/2)

mbm_tester = MBMSeriesTester(critical_surface=CriticalSurfaceMFBM(N=N, alpha=0.05))

To test if the series is MBM with a given holder exponent series h_mbm_series and use auto estimated sigma square:

is_mbm, sig2 = mbm_tester.test(h=h_mbm_series, x=series, sig2=None)

Be aware that MBMSeriesTester requires len(h_mbm_series)==len(series).

Use of cache

Use caching to speed up the testing process. If the series x for testing is unchanged and multiple h and/or sig2 are used, one may want to set is_cache_stat=True to allow cache variable stat. If h and sig2 are unchanged and multiple x are used, one may want to set is_cache_quantile=True to allow cache variable quantile.