The Python package `MFDFA` provides the tools to perform a multifractal detrended fluctuation analysis that enables the investigation of stochastic processes where long-range memory and persistence are necessary to consider.


What MFDFA can do for you


Various stochastic processes in nature are non-stationary (i.e., they possess a long-term memory) and additionally exhibit multifractal features, i.e., where the scaling behavior cannot be described by a single exponent.
Multifractal detrended fluctuation analysis is a valuable tool for analyzing stochastic processes and quantifying their correlations, scaling behavior and persistence.

The Python package MFDFA provides methods to perform this analysis, enabling the investigation of, for example, the study of long-range correlations and persistence.

It was developed at the Institute of Energy and Climate Research at the Forschungszentrum Jülich GmbH and is available at
Some basic examples of how to use the package are presented in the documentation found at
It can be installed via pip from PyPI (

A more detailed description of the package and the underlying theory can be found in the peer-reviewed paper published in Computer Physics Communications(DOI: 10.1016/j.cpc.2021.108254).


If you use MFDFA in your research, please cite it as:

Rydin Gorjão, L., Hassan, G., Kurths, J, and Witthaut, D. (2022). MFDFA: Efficient multifractal detrended fluctuation analysis in python. Computer Physics Communications, 273, 108254. DOI: 10.1016/j.cpc.2021.108254


L.R.G. kindly thanks Francisco Meirinhos for all the help with Python, and Fabian Harang, Marc Lagunas Merino, Anton Yurchenko-Tytarenko, Dennis Schroeder, Michele Giordano, Giulia di Nunno, and Fred Espen Benth for their support. L.R.G and D.W gratefully acknowledge support by the Helmholtz Association via the joint initiative Energy System 2050 - A Contribution of the Research Field Energy and the grant Uncertainty Quantification – From Data to Reliable Knowledge (UQ), with grant no. ZT-I-0029, the scholarship funding from E.ON Stipendienfonds, and the STORM - Stochastics for Time-Space Risk Models project of the Research Council of Norway (RCN) no. 274410. This work was performed as part of the Helmholtz School for Data Science in Life, Earth and Energy (HDS-LEE). J.K. was financed by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Center “Digital biodesign and personalised healthcare”, no. 075-15-2020-926.


Peng, C.-K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., & Goldberger, A. L. (1994). Mosaic organization of DNA nucleotides. Physical Review E, 49(2), 1685–1689 DOI: 10.1103/PhysRevE.49.1685
Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., & Stanley, H. E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and Its Applications, 316(1-4), 87–114 DOI: 10.1016/S0378-4371(02)01383-3

Programming language
  • Python 100%
  • MIT
</>Source code

Participating organisations

Forschungszentrum Jülich

Reference papers



Leonardo Rydin Gorjão
Norwegian University of Life Sciences