Nolds examples

You can run some examples for the functions in nolds with the command python -m nolds.examples <key> where <key> can be one of the following:

• lyapunov-logistic shows a bifurcation plot of the logistic map and compares the true lyapunov exponent to the estimates obtained with lyap_e and lyap_r.
• lyapunov-tent shows the same plot as lyapunov-logistic, but for the tent map.
• profiling runs a profiling test with the package cProfile.
• hurst-weron2 plots a reconstruction of figure 2 of the weron 2002 paper about the hurst exponent.
• hurst-hist plots a histogram of hurst exponents obtained for random noise.
• hurst-nvals creates a plot that compares the results of different choices for nvals for the function hurst_rs.

These tests are also available as functions inside the module nolds.examples.

Functions in nolds.examples

nolds.examples.plot_lyap(maptype=u'logistic')

Plots a bifurcation plot of the given map and superimposes the true lyapunov exponent as well as the estimates of the largest lyapunov exponent obtained by lyap_r and lyap_e. The idea for this plot is taken from [ll].

This function requires the package matplotlib.

References:

[ll]	Manfred Füllsack, “Lyapunov exponent”, url: http://systems-sciences.uni-graz.at/etextbook/sw2/lyapunov.html

Kwargs:

maptype (str):

can be either "logistic" for the logistic map or "tent" for the tent map.

nolds.examples.profiling()

Runs a profiling test for the function lyap_e (mainly used for development)

This function requires the package cProfile.

nolds.examples.weron_2002_figure2(n=10000)

Recreates figure 2 of [w] comparing the reported values by Weron to the values obtained by the functions in this package.

The experiment consists of n iterations where the hurst exponent of randomly generated gaussian noise is calculated. This is done with differing sequence lengths of 256, 512, 1024, …., 65536. The average estimated hurst exponent over all iterations is plotted for the following configurations:

• weron is the Anis-Lloyd-corrected Hurst exponent calculated by Weron
• rs50 is the Anis-Lloyd-corrected Hurst exponent calculated by Nolds with the same parameters as used by Weron
• weron_raw is the uncorrected Hurst exponent calculated by Weron
• rs50_raw is the uncorrected Hurst exponent calculated by Nolds with the same parameters as used by Weron
• rsn is the Anis-Lloyd-corrected Hurst exponent calculated by Nolds with the default settings of Nolds

The values reported by Weron are only measured from the plot in the PDF version of the paper and can therefore have some small inaccuracies.

This function requires the package matplotlib.

References:

[w]	R. Weron, “Estimating long-range dependence: finite sample properties and confidence intervals,” Physica A: Statistical Mechanics and its Applications, vol. 312, no. 1, pp. 285–299, 2002.

Kwargs:

n (int):

number of iterations of the experiment (Weron used 10000, but this takes a while)

nolds.examples.plot_hurst_hist()

Plots a histogram of values obtained for the hurst exponent of uniformly distributed white noise.

This function requires the package matplotlib.

nolds.examples.hurst_compare_nvals(data, nvals=None)

Creates a plot that compares the results of different choices for nvals for the function hurst_rs.

Args:

data (array-like of float):

the input data from which the hurst exponent should be estimated

Kwargs:

nvals (array of int):

a manually selected value for the nvals parameter that should be plotted in comparison to the default choices