FluctuationAnalysisTools 1.9.0

This library allows to create and process long-term dependent datasets.

StatTools

This library allows to create and process long-term dependent datasets.

Installation

You can install FluctuationAnalysisTools from PyPI.

pip install FluctuationAnalysisTools

Or you can clone the repository and build it using the command

pip install .

Examples

You can find examples and published usages in the folder Research

If you used the project in your paper, you are welcome to ask us to add reference via a Pull Request or an Issue.

Basis usage

1. To create a simple dataset with given Hurst parameter:

from StatTools.filters import FilteredArray

h = 0.8                 # choose Hurst parameter
total_vectors = 1000    # total number of vectors in output
vectors_length = 1440   # each vector's length
t = 8                   # threads in use during computation

correlated_vectors = Filter(h, vectors_length).generate(n_vectors=total_vectors,
                                                        threads=t, progress_bar=True)

Generators

1. Example of sequence generation based on the Hurst exponent.

from StatTools.generators.hurst_generator import LBFBmGenerator
h = 0.8             # choose Hurst parameter
filter_len = 40     # length of the optimized filter
base = 1.2          # the basis for the filter optimization algorithm
target_len = 4000   # number of generation iterations

generator = LBFBmGenerator(h, filter_len, base)
signal = []
for value in islice(generator, target_len):
    signal.append(value)

For more information and generator validation, see lbfbm_generator.ipynb.

It is also possible to use the method of generating increments with a given H using KasdinGenerator.

from StatTools.generators.kasdin_generator import KasdinGenerator
h = 0.8             # choose Hurst parameter
target_len = 4000   # number of generation iterations

generator = KasdinGenerator(h, length=target_len)

# the first option
signal = generator.get_full_sequence()

# the second option
signal_list = []
for sample in generator:
    signal_list.append(sample)

For more information see Kasdin, N. J. (1995). Discrete simulation of colored noise and stochastic processes and 1/f/sup /spl alpha// power law noise generation. doi:10.1109/5.381848.

Fluctuational Analysis

1. Example of Detrended Fluctuational Analysis (DFA)

from StatTools.generators.base_filter import Filter
from StatTools.analysis.dfa import DFA

h = 0.7 # choose Hurst parameter
length = 6000 # vector's length
target_std = 1.0
target_mean = 0.0

generator = Filter(h, length, set_mean=target_mean, set_std=target_std)
trajectory = generator.generate(n_vectors=1)

actual_mean = np.mean(trajectory)
actual_std = np.std(trajectory, ddof=1)
actual_h = DFA(trajectory).find_h()
print(actual_h) # Should print a value close to 0.7

Contributors

• Alexandr Kuzmenko
• Aleksandr Sinitca
• Asya Lyanova