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Multifractal detrended fluctuation analyses

version 1.0 (7.04 MB) by

The multifractal



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In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal by computing alpha (or Hurst exponent H).It is useful for analysing time series that appear to be long-range dependent processes. However, the conventional DFA only scale the second order statistical moment and assumes that the process are normal distributed. MFDFA1 and MFDFA2 in the present zip-folder computes the H(q) for all q-order statistical moments as well as the local Hurst exponent H(t). Furthermore, H(q) and H(t) are also used to compute the multifractal spectrum D(h) by a legendre transform of H(q) or directly from the histogram of H(t).

If the codes are used in scientific publications please cite Ihlen (2012) contained in the zip-folder.

Modifications of MFDFA code with wavelet and EMD detrending are availible at

Comments and Ratings (7)

please i can't adapt the code with my data, may aim is to show mutlifractality on financial time series, can someone send me the code or give me some idea to adapt it.


uday (view profile)

How can I implement two dimensional DFA using this code. Thank you

Hal Knowles

Truly incredible research, coding, and generosity in sharing the work!

Yan Jiang

Absolute fantastic work!

xiuling yu

Faiza Bukenya

Thank you so much for the code. if i want to segment images. How do i use multifractal to segment the images.


Very elaborate tutorial! Great works.

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