DFA

class fathon.DFA(tsVec)

Bases: object

Detrended Fluctuation Analysis class.

Parameters:tsVec (iterable) – Time series used for the analysis.
computeFlucVec(winSizes, polOrd=1, revSeg=False, unbiased=False)

Computation of the fluctuations in each window.

Parameters:
  • winSizes (numpy ndarray) – Array of window’s sizes.
  • polOrd (int, optional) – Order of the polynomial to be fitted in each window (default : 1).
  • revSeg (bool, optional) – If True, the computation of F is repeated starting from the end of the time series (default : False).
  • unbiased (bool, optional) – If True, the unbiased version of DFA is computed, and revSeg is ignored. To be used on short time series (default : False).
Returns:

  • numpy ndarray – Array n of window’s sizes.
  • numpy ndarray – Array F containing the values of the fluctuations in each window.
fitFlucVec(nStart=-999, nEnd=-999, logBase=2.718281828459045, verbose=False)

Fit of the fluctuations values.

Parameters:
  • nStart (int, optional) – Size of the smaller window used to fit F (default : first value of n).
  • nEnd (int, optional) – Size of the bigger window used to fit F (default : last value of n).
  • logBase (float, optional) – Base of the logarithm for the log-log fit of n vs F (default : e).
  • verbose (bool, optional) – Verbosity (default : False).
Returns:

  • float – Slope of the fit.
  • float – Intercept of the fit.
multiFitFlucVec(limitsList, logBase=2.718281828459045, verbose=False)

Fit of the fluctuations values in different intervals at the same time.

Parameters:
  • limitsList (numpy ndarray) – kx2 array with the sizes of k starting and ending windows used to fit F.
  • logBase (float, optional) – Base of the logarithm for the log-log fit of n vs F (default : e).
  • verbose (bool, optional) – Verbosity (default : False).
Returns:

  • numpy ndarray – Slopes of the fits.
  • numpy ndarray – Intercepts of the fits.
saveObject(outFileName)

Save current object state to binary file.

Parameters:outFileName (str) – Output binary file. .fathon extension will be appended to the file name.

Usage examples

import numpy as np
import fathon
from fathon import fathonUtils as fu

#time series
a = np.random.randn(10000)

#zero-mean cumulative sum
a = fu.toAggregated(a)

#initialize dfa object
pydfa = fathon.DFA(a)
#compute fluctuation function and Hurst exponent
wins = fu.linRangeByStep(10, 2000)
n, F = pydfa.computeFlucVec(wins, revSeg=True, polOrd=3)
H, H_intercept = pydfa.fitFlucVec()

#compute Hurst exponent in different ranges
limits_list = np.array([[15,2000], [200,1000]], dtype=int)
list_H, list_H_intercept = pydfa.multiFitFlucVec(limits_list)