PyConnectedness

⚠️ Active development. This library is currently under active development. The API and project structure may still change as additional connectedness and dependence methods are added.

About

PyConnectedness is a Python library for analysing connectedness, spillovers and dependence in multivariate (time series) data. The current implementation focuses on variance-decomposition-based connectedness measures in the spirit of Diebold and Yilmaz (2009, 2012, 2014), including static and rolling-window dynamic connectedness, directional spillovers, net spillovers, net pairwise directional connectedness, and graphical representations of connectedness networks. Additionally, the package implements the frequency-domain connectedness framework of Baruník and Křehlík (2018), allowing connectedness to be decomposed across different frequency bands and time horizons. A max-linear Bayesian network module is additionally in progress, aiming to extend the package towards modelling extremal dependence and causal structures between extreme events. The goal is to bring methods that are well established in econometrics, statistics and applied mathematics, but still scattered or missing in Python, into one open-source package.

Project status

• Connectedness and spillover analysis
  Static and rolling-window dynamic connectedness, directional TO and FROM, net and pairwise_net directional connectedness.

• Visualisation Spillover heatmaps and directed connectedness networks.

• Frequency-domain connectedness
  Analysis of spillovers across different time horizons.

• Max-linear Bayesian networks Modelling extremal dependence and causal structures between extreme events.

• Animations Animated heatmaps, networks and time series (next release)

Installation

PyConnectedness requires Python 3.10 or newer.

Install from PyPI:

pip install pyconnectedness

Usage

PyConnectedness provides a compact interface for estimating VAR-based connectedness measures.

A static connectedness estimate can be computed directly from a pandas DataFrame using a simple one-liner:

from pyconnectedness import static_connectedness

result = static_connectedness(
    data,
    horizon=10,
    method="generalized",
    lags=2,
)

print(result.table)
print(result.total)
print(result.directional_to)
print(result.directional_from)
print(result.net)
print(result.pairwise_net)

For Diebold-Yilmaz (2009) - an orthogonalized Cholesky variance decomposition can be used:

result = static_connectedness(
    data,
    horizon=10,
    method="orthogonalized",
    lags=2,
)

Rolling-window connectedness is available through:

from pyconnectedness import dynamic_connectedness

dynamic = dynamic_connectedness(
    data,
    window=200,
    horizon=10,
    method="generalized",
    lags=2,
)

print(dynamic.total)
print(dynamic.net)

Frequency connectedness splits the spillover table into bands:

from pyconnectedness import frequency_connectedness

frequency = frequency_connectedness(
    data,
    horizon=100,
    periods=(5, 20),
    method="generalized",
    lags=4,
)

print(frequency.total)
print(frequency.within)
print(frequency.share)

The package currently provides:

• VAR estimation and moving-average representations
• orthogonalized forecast error variance decomposition
• generalized forecast error variance decomposition
• static connectedness measures
• rolling-window dynamic connectedness
• total connectedness
• directional TO and FROM measures
• net directional connectedness
• net pairwise directional connectedness
• frequency-domain connectedness
• within-frequency connectedness
• spillover heatmaps
• directed connectedness networks

Preview: animations (next release)

The next version will add animated versions of the figures, built up step by step, or played back one rolling window per frame.

For complete examples, see the replication notebooks below.

Replication of Diebold-Yilmaz papers

The examples/ directory contains end-to-end replications of the main Diebold-Yilmaz connectedness frameworks using the PyConnectedness package, providing reproducible examples and validation against published results.

Diebold-Yilmaz (2009)

The DY-2009 replication uses the orthogonalized, Cholesky-based variance decomposition and reproduces the static and dynamic spillover analysis using the original framework.

Source notebook:

examples/replicate_dy2009.ipynb

Or with Colab:

Diebold-Yilmaz (2012)

The DY-2012 replication uses the generalized forecast error variance decomposition and the corresponding row-normalized connectedness framework.

Source notebook:

examples/replicate_dy2012.ipynb

These notebooks also serve as reproducible usage examples for the package.

Repository structure

pyconnectedness/
├── README.md
├── LICENSE                     # GPLv3
├── pyproject.toml              # packaging & dependencies
├── .gitignore
├── .github/
│   └── workflows/
│       └── tests.yml           # continuous integration
├── src/
│   └── pyconnectedness/        # the library source code
│       ├── __init__.py
│       ├── connectedness/      # Diebold-Yilmaz spillover measures
│       ├── causality/          # max-linear Bayesian networks (in development)
│       └── viz/                # network plotting
├── tests/                      # unit tests
├── examples/                   # example notebooks
├── CITATION.cff                # citation
└── logos/                      # project & funding logos

References

The methods draw on, among others:

• Diebold and Yilmaz (2009, 2012, 2014) for variance-decomposition-based connectedness and spillover measures
• Baruník and Křehlík (2018) for frequency-domain connectedness
• Gissibl and Klüppelberg (2018) for max-linear models on directed acyclic graphs

(Reference list to be completed as the modules are implemented.)

Data

The data files in this directory are used for replication and validation of the connectedness measures implemented in PyConnectedness.

Diebold-Yilmaz (2009)

The files

• dy2009_returns.xlsx
• dy2009_vola.xlsx

are based on the DY2009 data distributed with:

Nguyen, Viet Hoang; Kocenda, Evzen; Greenwood-Nimmo, Matthew (2024), "Detecting Statistically Significant Changes in Connectedness: A Bootstrap-based Technique", Mendeley Data, V1.

DOI: https://doi.org/10.17632/rtwsfgpgmf.1

Diebold-Yilmaz (2012)

The file

• dy2012_vola.xlsx

is based on the replication material available from:

Doan, Tom (2025), "DIEBOLDYILMAZ_IJF2012: RATS program to replicate Diebold and Yilmaz (2012) spillover calculations."

EconPapers: https://econpapers.repec.org/software/bocbocode/rtz00199.htm

Funding

Developed with support from the Prototype Fund (Software Sprint), funded by the German Federal Ministry of Research, Technology and Space (BMFTR) and supported by the Open Knowledge Foundation Deutschland.

License

Released under the GNU General Public License v3.0 or later.