Multifractal detrended fluctuation analyses

The multifractal

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 www.ntnu.edu/inm/geri/software