Copulas – Theory & Project with R

Access

Video lectures from this course are available as a YouTube playlist and are being released progressively.

Copulas – Theory & Project with R (YouTube playlist)

Course Overview

Copulas – Theory & Project with R is designed to introduce you to copula theory and its applications in statistical modeling using R. This course provides a structured approach to understanding copulas, from fundamental concepts to hands-on implementation with toy data.

This is an introductory crash course, not an advanced or research-level treatment.

Learning Outcomes

• Understand the fundamentals of copulas and their role in modeling dependence structures.
• Explore Sklar’s Theorem and the decomposition of joint CDFs into marginals and a copula.
• Learn representative copula families: Gaussian, Student-t, Clayton, and Gumbel.
• Estimate copula parameters in R using the copula package.
• Evaluate fitted models using log-likelihood, AIC, and BIC.
• Visualize copulas using scatter plots, contour plots, and 3D surfaces.
• Simulate data using fitted copula models.
• Analyze dependence using Kendall’s tau, Spearman’s rho, and tail dependence coefficients.

Components of the Course

The course is organized into three closely connected blocks.

Block 1 — Companion Materials

Illustrative datasets

• Dataset 01: copula_data_01.csv | copula_data_01.xlsx
• Dataset 02: copula_data_02.csv | copula_data_02.xlsx
• Dataset 03: copula_data_03.csv | copula_data_03.xlsx
• Dataset 04: copula_data_04.csv | copula_data_04.xlsx

Project and reference materials

• Introductory notes: copulas_introductory_notes.pdf
• Project document: copulas_project.pdf
• Probabilistic formulas: copulas_probailistic_formulas.pdf
• R script (project code): copulas_project.r

Block 2 - A Brief Guide to Four Fundamental Copulas

• Intro – Copulas. At Least Some of Them
• Copulas Explained: Basic Characteristics
• d-Dimensional Copula Function
• Interactive 3D Plot: Basic Properties of a Bivariate Copula
• Sklar’s Theorem
• Elliptical Copulas: Multivariate Gaussian Copula
• Elliptical Copulas: Bivariate Gaussian Copula
• Gaussian Copula: Scatter Plots
• Elliptical Copulas: Multivariate t-Copula
• Elliptical Copulas: Bivariate t-Copula
• t-Copula: Scatter Plots
• Archimedean Copulas: Multivariate Clayton Copula
• Archimedean Copulas: Bivariate Clayton Copula
• Clayton Copula: Scatter Plots
• Archimedean Copulas: Multivariate Gumbel Copula
• Archimedean Copulas: Bivariate Gumbel Copula
• Gumbel Copula: Scatter Plots
• Tail Dependence
• Correlation
• Interactive Scatter Plots: Gaussian, t, Clayton, and Gumbel
• t-Copula: Spearman’s rho vs Correlation Parameter (df = 10, simulation)
• Clayton Copula: Spearman’s rho vs Clayton Parameter
• Gumbel Copula: Spearman’s rho vs Gumbel Parameter

Block 3 - Study of Two-Dimensional Distributions of Random Variable Using R copula package

• Copula R Project
• R Packages
• Data Import
• Data Visualization
• Independence Test of Random Variables
• Data Transformation
• Copula Parameter Estimation
• Analysis of Estimated Parameters
• Verification of Fit Quality of Parameters
• Selection of the Best Copula
• Visual Analysis of the Copula
• Analysis of Correlation Dependencies
• Data Simulation
• Probability Calculations

Terminology note: In some videos, the term “t-Student” is used; this corresponds to the standard English term “Student-t”.

Instructor

Dr Krzysztof Ozimek, PRM

This course reflects over 30 years of experience teaching quantitative finance, statistics, and analytical tools.

The content is science-based and designed to emphasize clarity, methodological soundness, and practical interpretation.

For educational purposes only. Not financial advice.

Accessibility

Video lectures include auto-generated captions provided by YouTube — please note these may contain errors or inaccuracies.