How to estimate copula parameters from real data using pseudo-observations and Kendall's tau — the practical bridge between theory and application.
We cover the key preprocessing step of transforming data to pseudo-observations via normalized ranks, then derive closed-form parameter estimates for Gaussian (ρ = sin(τπ/2)), Clayton (α = 2τ/(1-τ)), and Gumbel (α = 1/(1-τ)) copulas. For the Frank copula, we use numerical root-finding with the Debye function. All methods are validated on synthetic data to confirm recovery of true parameters.
Part 8 of 14 in the Copula Short Course.
Follow along with the Jupyter notebook:
https://github.com/kkarrancsu/copula-short-course/blob/main/notebooks/8_fittingdata.ipynb
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📓 Get the full course materials: https://kirantrillium.gumroad.com/l/copula-course
Includes 14 interactive Jupyter notebooks, 4 real-world case studies, 17 exercises with solutions, and code templates.
