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TIME SERIES ALGORITHM


Detrending Moving Average (DMA) Algorithm for Time Series (d=1 long range correlated sequences)



The DMA algorithm allows the calculation of the:

(a) global Hurst exponent of long range correlated time series according to the method proposed in :
Second-order moving average and scaling of stochastic time series,
Eur. J. Phys. B, 27, 197, (2002)

(b) local Hurst exponent of long range correlated time series according to the method proposed in :
Time-Dependent Hurst Exponent in Financial Time Series
Physica A, 344, 267, (2004)


Click here to download the package "series.zip" including executables and configuration files


The folder "series.zip" contains the following files:

(1) DMA_Algorithm.exe [This is the executable program for the DMA algorithm. It is possible to use: (i) the simple DMA (see E.Alessio et al. EPJB 2002), (ii) the dynamic DMA (see A. Carbone et al. Physica A 2004), (iii) shifted DMA means that you can set the reference point of the moving average at an arbitrary point of the window, e.g. 1st, middle, last.

(2) Configuration.txt (this is the configuration file with the parameters used by the executable program (1).) The parameters must be changed according to the signal you have to analyse. Now the parameters are those working for the signal included in the folder(5)

(3) Artificial_H=0.5-1.txt (Artificially Fractional Brownian signal with Hurst exponent H=0.5 generated by the Random Midpoint Displacement Algorithm)

(4) Output DMA (2).out.txt (Contains 4 quantities: the input file name; the number of samples of the signals one wants to use, the starting point of the calculation, the end point of the calculation, the Hurst exponent obtained 0.53)

(5) Output DMA (2).out.txt.Artificial_H=0.5-1.txt.chart.txt (1st col.: "n"; 2nd col. "sigma_DMA"; 3rd col. "log n"; 4th col. "log sigma_DMA")

(6) progression-3.txt, progression-4.txt and progression-5.txt (these files are two examples of choices of the moving average window that one can choose instead of the linear choice (start, step, end))


To implement the DMA calculation:

a) run the program DMA_Algorithm.exe:
b) load the file Configuration.txt by clicking on the "load" button
c) check that all the parameters are ok (especially the input and output file paths! )
c) press the "calculate" button.
d) two ouput files as (4) and (5) will be obtained.


Click here to download the package "series.zip" including executables and configuration files.