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DFA: MATLAB function to compute the Hurst exponent using Detrended Fluctuation Analysis (DFA)


  • Rafal Weron


H = DFA(X) calculates the Hurst exponent of time series X using Detrended Fluctuation Analysis (DFA). If a vector of increasing natural numbers is given as the second input parameter, i.e. DFA(X,D), then it defines the box sizes that the sample is divided into (the values in D have to be divisors of the length of series X). If D is a scalar (default value D = 10) it is treated as the smallest box size that the sample can be divided into. In this case the optimal sample size OptN and the vector of divisors for this size are automatically computed. OptN is defined as the length that possesses the most divisors among series shorter than X by no more than 1%. The input series X is truncated at the OptN-th value. [H,PV95] = DFA(X) returns the empirical confidence intervals PV95 at the 95% level (see [2]). [H,PV95,P] = DFA(X) returns the average standard deviations P of the detrended walk for all the divisors.

Suggested Citation

  • Rafal Weron, 2011. "DFA: MATLAB function to compute the Hurst exponent using Detrended Fluctuation Analysis (DFA)," HSC Software M11002, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:hscode:m11002

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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. The stock market and happiness
      by UDADISI in UDADISI on 2012-08-01 23:55:00


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    Cited by:

    1. Tonzer, Lena, 2017. "Uncertainty, financial crises, and subjective well-being," IWH Discussion Papers 2/2017, Halle Institute for Economic Research (IWH).
    2. Anita Ratcliffe & Karl Taylor, 2013. "Who Cares about Stock Market Booms and Busts? Evidence from Data on Mental Wellbeing," Working Papers 2012021, The University of Sheffield, Department of Economics.
    3. Frijters, Paul & Johnston, David W. & Shields, Michael A. & Sinha, Kompal, 2015. "A lifecycle perspective of stock market performance and wellbeing," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 237-250.


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