Unbalanced Wasserstein Barycenter for Energy Markets

Implementation of the paper: "Information-driven modeling of energy markets: an unbalanced Wasserstein barycenter approach"

Authors: Carlo Mari, Emiliano Mari, Cristiano Baldassari (University of Tuscia; Sydus)

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Overview

This repository implements the 5-step pipeline described in the paper to analyze natural gas and electricity prices:

Step 1: Preprocessing

Inject and compute normalized detrended log-returns

Step 2: Visibility Graphs

Transform time series into graphs

Step 3: Embeddings

Represent graphs in 128 dimensions (Diff2Vec)

Step 4: Wasserstein Barycenter

Compute optimal fusion: λ_gas = 0.65, λ_el = 0.35

Step 5: Gaussian Mixture Model

Model joint distribution

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Quick Start

Install Dependencies

pip install numpy pandas matplotlib scipy statsmodels POT networkx karateclub ts2vg scikit-learn jupyter

Run Notebooks

jupyter notebook

Execute in order:

1. 01_preprocessing.ipynb - Load data, detrending with LOESS, detrended and and normalized log-returns
2. 02_visibility_graphs.ipynb - Build graphs
3. 03_embeddings.ipynb - Diff2Vec embeddings
4. 04_wasserstein.ipynb - Optimal barycenter
5. 05_gmm.ipynb - Final model

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Data

Data already included andav available freely on mercatoelettrico.org

Files in data/:

• logret_gas.dat - Natural gas log-returns (2019-2023)
• logret_electricity.dat - Electricity log-returns (2019-2023)

1825 observations already preprocessed with LOESS. Ready to use!

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Main Result

The method automatically finds:

• Natural gas weight: 65% (dominant)
• Electricity weight: 35%

This reflects the European market structure!

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Contact

• Cristiano Baldassari: cristiano.baldassari@unitus.it

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License

MIT License - Feel free to use this code