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Multifractal Detrended Fluctuation Analysis in Python

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In [Faini 2021](https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2020.0254), they suggest a "seemingly simple" modification of the equation for when q = 0 ![image](https://user-images.githubusercontent.com/8875533/179874501-1130e225-e6bf-49bf-8b79-53e9fe772792.png) Currently it seems like we [do](https://github.com/neuropsychology/NeuroKit/blob/4893241284f25d481d3e4afde6d8632d68f7e40c/neurokit2/complexity/fractal_dfa.py#L493): ``` python fluctuation = np.float_power(np.mean(np.float_power(var, q...

enhancement

A recent paper in Physica A, entitled [A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation](https://doi.org/10.1016/j.physa.2020.125611) (Physica A 565, p125611, 2021) suggests a set of "complicated"...

enhancement

When I designed `MFDFA` I had an eye on how to handle missing data, so the code if capable of handling `numpy` `masked` arrays, which is pretty nice, since we...

documentation

In *A DFA approach for assessing asymmetric correlations*, by Jose Alvarez-Ramirez, Eduardo Rodriguez, and Juan Carlos Echeverria, have "[...] developed a DFA extension for exploring the existence of asymmetries in...

enhancement

We should run some performance tests to see how `MFDFA` with all the extensions is running. This should include: - [ ] standard MFDFA (i.e., no extensions) - [ ]...

An interesting, similar (in nature), Multifractal Cross-Correlation Analysis (MFCXA) is presented by Qingju Fan and Dan Li, _Modeling electricity prices: jump diffusion and regime switching_, [Physica A, 429, 17-27, 2015](https://doi.org/10.1016/j.physa.2015.02.065)...

enhancement

Include a Singularity spectrum code to understand the strength of the multifractality of the timeseries: ![Screenshot from 2020-07-03 17-57-57](https://user-images.githubusercontent.com/47757762/86484600-dc5ad980-bd56-11ea-8606-92fcf3b92d4e.png) This is found in: [Multifractal detrended fluctuation analysis of nonstationary time...

enhancement