nolds: Nonlinear Measures for Dynamical Systems in Python

Introduction

nolds is a small, numpy-based Python library designed for implementing and learning about nonlinear measures for dynamical systems, specifically based on one-dimensional time series. It offers a comprehensive suite of tools for analyzing the complexity, predictability, and memory of time series data.

Key measures implemented in nolds include:

• Sample Entropy (sampen): Measures time-series complexity.
• Correlation Dimension (corr_dim): Quantifies the fractal dimension and complexity.
• Lyapunov Exponent (lyap_r, lyap_e): Indicates chaos and unpredictability in a system.
• Hurst Exponent (hurst_rs): Measures long-term memory, useful for analyzing trends.
• Detrended Fluctuation Analysis (DFA): Estimates the Hurst parameter for non-stationary processes.
• Generalized Hurst Exponent (mfhurst_b): A generalization for multifractal data series.

Installation

nolds supports Python 2 (>= 2.7) and Python 3 (>= 3.4) and primarily requires the numpy package.

You can easily install nolds using pip:

pip install nolds

Optional dependencies for extended functionality include sklearn for RANSAC line fitting, quantumrandom for true random numbers, and matplotlib for plotting functions in nolds.examples.

Examples

Here's a quick example demonstrating how to use nolds to calculate the Detrended Fluctuation Analysis (DFA) for a random walk:

import nolds
import numpy as np

rwalk = np.cumsum(np.random.random(1000))
h = nolds.dfa(rwalk)
print(f"Hurst parameter (DFA): {h}")

Why Use nolds?

nolds stands out as a valuable tool for researchers and developers working with time series data due to several reasons:

• Comprehensive Measures: It provides a wide array of nonlinear measures, from entropy to fractal dimensions and Lyapunov exponents, all in one library.
• Learning Resource: Each function comes with extensive documentation explaining the algorithm and pointing to relevant academic papers, making it an excellent educational tool.
• Non-Stationary Data: Its Detrended Fluctuation Analysis (DFA) is particularly useful for analyzing non-stationary processes, which are common in real-world data like financial markets.
• Pythonic and NumPy-based: Built on NumPy, nolds integrates seamlessly into the Python scientific computing ecosystem, ensuring efficiency and ease of use.

Links

• GitHub Repository: CSchoel/nolds
• HTML Documentation: nolds Documentation
• Read the Docs: nolds on Read the Docs
• Zenodo Reference: Cite nolds