A Python library for creating and processing long-term dependent datasets, with a focus on statistical analysis tools for fluctuation analysis, time series generation, and signal processing.
- Synthetic Data Generation: Create datasets with controlled statistical properties (Hurst exponent, long-term dependencies)
- Fluctuation Analysis: Perform Detrended Fluctuation Analysis (DFA), Detrended Partial Cross-Correlation Analysis (DPCCA), and other methods
- Signal Processing: Apply filters and transformations to time series data
- Research Tools: Support scientific research in complex systems exhibiting long-range correlations
- Performance Optimized: Multi-threaded implementations with C++ extensions for large datasets
You can install StatTools from PyPI:
pip install FluctuationAnalysisToolsOr clone the repository and install locally:
git clone https://github.com/Digiratory/StatTools.git
cd StatTools
pip install .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.
from StatTools.generators.base_filter import FilteredArray
import numpy as np
# Create a dataset with Hurst exponent H = 0.8
h = 0.8
total_vectors = 1000
vectors_length = 1440
threads = 8
# Generate correlated vectors
generator = FilteredArray(h, vectors_length)
correlated_vectors = generator.generate(n_vectors=total_vectors, threads=threads, progress_bar=True)
print(f"Generated {len(correlated_vectors)} vectors of length {len(correlated_vectors[0])}")from StatTools.analysis.dfa import DFA
import numpy as np
# Generate sample data
np.random.seed(42)
data = np.random.randn(10000)
# Perform Detrended Fluctuation Analysis
dfa = DFA(data)
hurst_exponent = dfa.find_h()
print(f"Estimated Hurst exponent: {hurst_exponent:.3f}")from StatTools.generators.lbfbm_generator import LBFBmGenerator
# Parameters
hurst_exponent = 0.8 # H ∈ (0, 2)
base = 1.2
sequence_length = 4000
# Create and use generator
generator = LBFBmGenerator(h=hurst_exponent, base=base, length=sequence_length)
signal = list(generator)
print(f"Generated signal of length {len(signal)}")For more details, see lbfbm_generator.ipynb.
from StatTools.generators.kasdin_generator import KasdinGenerator
h = 0.8
target_len = 4000
generator = KasdinGenerator(h, length=target_len)
# Generate full sequence
signal = generator.get_full_sequence()
print(f"Generated signal: {signal[:10]}...") # First 10 values
# Or iterate through samples
signal_list = []
for sample in generator:
signal_list.append(sample)Reference: Kasdin, N. J. (1995). Discrete simulation of colored noise and stochastic processes and 1/f^α power law noise generation. DOI:10.1109/5.381848.
from StatTools.generators.base_filter import Filter
from StatTools.analysis.dfa import DFA
import numpy as np
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)[0] # Get the first (and only) trajectory
actual_mean = np.mean(trajectory)
actual_std = np.std(trajectory, ddof=1)
actual_h = DFA(trajectory).find_h()
print(f"Estimated H: {actual_h:.3f} (Expected: {h:.3f})")FilteredArray: Base class for generating correlated datasetsLBFBmGenerator: Linear Fractional Brownian Motion generatorKasdinGenerator: Colored noise generator using Kasdin's methodFieldGenerator: Spatial data generator
DFA: Detrended Fluctuation AnalysisDPCCA: Detrended Partial Cross-Correlation AnalysisFA: Fluctuation AnalysisQSS: Quantile Segmentation Statistics
KalmanFilter: Kalman filtering implementation
Find comprehensive examples and published research in the research/ folder:
If you've used StatTools in your research, consider contributing your examples via a Pull Request or Issue.
We welcome contributions! Please see our Contributing Guide for details on:
- Setting up a development environment
- Code style and standards
- Testing guidelines
- Submitting pull requests
This project is licensed under the terms specified in LICENSE.txt.
If you use StatTools in your research, please cite:
@software{statttools,
title = {StatTools: A Python Library for Long-term Dependent Dataset Analysis},
author = {Kuzmenko, Alexandr and Sinitca, Aleksandr and Lyanova, Asya},
url = {https://github.com/Digiratory/StatTools},
version = {1.6.1}
}See CHANGELOG.md for version history and updates.