Replication code for "Directional Dependence of Extreme Events" by Maxime L. D. Nicolas and Matthieu Garcin.
This repository contains the Jupyter notebooks required to replicate all figures and tables in the paper. Each notebook corresponds to a self-contained step of the analysis, with step-by-step instructions embedded in the cells.
| # | Notebook | Purpose |
|---|---|---|
| 1 | 1_khoudraji_copula.ipynb |
Defines the Khoudraji copula construction and computes theoretical TCTEs ( |
| 2 | 2_simulations_khoudraji.ipynb |
Runs the Monte Carlo simulation study under Khoudraji's device; computes bias and RMSE of the estimators — reproduces Tables 2–4 and Figures 2–5 |
| 3 | 3_asymtotic_results.ipynb |
Numerically verifies the asymptotic normality of the estimator and plots the asymptotic variance, bias, and quadratic risk as functions of the threshold |
| 4 | 4_variance_estimator.ipynb |
Implements the empirical variance and covariance estimators |
| 5 | 5_simulations_skewt.ipynb |
Runs the simulation study under the skew-$t$ copula with varying skewness parameters; reports empirical power of the directional dependence test — reproduces Table 5 and Figure 6 |
| 6 | 6_process_ocean_data.ipynb |
Downloads and processes NDBC buoy 46001 data (1976–2025): subsamples to weekly frequency, removes seasonality, tests autocorrelation, and produces summary statistics and empirical copula plots — reproduces Table 6 and Figure 7 |
| 7 | 7_testing_ocean_data.ipynb |
Applies the directional tail dependence test to all pairs of ocean variables; constructs the directed dependency networks — reproduces Table 7 and Figures 8–9 |
The notebooks run on Python 3.9+. Install dependencies with:
pip install numpy scipy pandas matplotlib statsmodels networkx joblib requests sympyRun the notebooks in order. Notebooks 2, 5, and 7 import 4_variance_estimator.ipynb via %run, so no manual setup is needed beyond running each notebook top to bottom.
Ocean data (notebook 6) is downloaded automatically from the NOAA NDBC public API.